Document:

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                                                                   EXHIBIT 10.17

Note: Redacted portions have been marked with (***). The redacted portions are
subject to a request for confidential treatment that has been filed with the
Securities and Exchange Commission.

                              WARRANT CERTIFICATE

                                 TELLIUM, INC.

                                "A" WARRANTS TO
                             PURCHASE COMMON STOCK

Certificate                                                      Certificate for
No. 1                                                     1,000,000 "A" Warrants

     THIS WARRANT CERTIFICATE CERTIFIES THAT U.S. TELESOURCE, INC., a Delaware
corporation ("U.S. Telesource"), or its registered assigns, is the registered
holder of the number of "A" Warrants (the "Warrants") set forth above which were
sold and granted to U.S. Telesource pursuant to the Warrant Purchase Agreement,
dated as of the date hereof, between U.S. Telesource and TELLIUM, INC., a
Delaware corporation (the "Company").  Each Warrant entitles the holder thereof
to subscribe for and purchase one fully paid and nonassessable share of common
stock, par value $.001 per share (the "Common Stock") (as adjusted pursuant to
Section 5, a "Warrant Share") of the Company, at any time and from time to time
after the date such Warrant becomes exercisable pursuant to Section 4.1 and
prior to the Expiration Time, at the purchase price of $30.00 per share (as such
price may be adjusted pursuant to Section 5, the "Warrant Price"), subject to
the provisions and upon the terms and conditions hereinafter set forth. Terms
not otherwise defined herein have the meanings stated in Section 24.

         THE SECURITIES REPRESENTED BY THIS CERTIFICATE HAVE BEEN
         ACQUIRED FOR INVESTMENT AND HAVE NOT BEEN REGISTERED UNDER
         THE SECURITIES ACT OF 1933. THESE SECURITIES MAY NOT BE SOLD
         OR TRANSFERRED IN THE ABSENCE OF SUCH REGISTRATION OR AN
         EXEMPTION THEREFROM UNDER SAID ACT. ADDITIONALLY, THE
         TRANSFER OF THESE SECURITIES IS SUBJECT TO THE CONDITIONS
         SPECIFIED IN SECTION 7 OF THE WARRANT PURCHASE AGREEMENT, AND
         NO TRANSFER OF THESE SECURITIES SHALL BE VALID OR EFFECTIVE
         UNTIL SUCH CONDITIONS HAVE BEEN FULFILLED. UPON THE
         FULFILLMENT OF CERTAIN SUCH CONDITIONS, THE SECRETARY OF
         TELLIUM, INC. HAS AGREED TO DELIVER TO THE HOLDER HEREOF A
         NEW CERTIFICATE, NOT BEARING THIS LEGEND, FOR THE SECURITIES
         REPRESENTED HEREBY REGISTERED IN THE NAME OF THE HOLDER
         HEREOF. COPIES OF SUCH AGREEMENT MAY BE OBTAINED AT NO COST
         BY WRITTEN REQUEST MADE BY THE HOLDER OF RECORD OF THIS
         CERTIFICATE TO THE SECRETARY OF TELLIUM, INC.
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1.   Vesting of Warrants.
     -------------------

     Pursuant to the Warrant Purchase Agreement, the Company sold and granted
the Warrants to U.S. Telesource.  Each Warrant is fully vested, shall be subject
to adjustment pursuant to Section 5, and shall become exercisable as set forth
in Section 4.

2.   Transferability of Warrants.
     ---------------------------

     2.1  Warrant Register and Registration.  The Secretary of the Company will
          ---------------------------------
          keep or cause to be kept at the office of the Company books for the
          registration and transfer (the "Warrant Register") of this Warrant
          Certificate and any other Warrant certificate issued hereunder
          (collectively, including the initial Warrant, the "Warrants").  The
          Warrant Certificates will be numbered and will be registered in the
          Warrant Register as they are issued.  The Company and the Secretary of
          the Company will be entitled to treat a person as the owner in fact
          for all purposes of each Warrant registered in such person's name
          (each registered owner is herein referred to as a "holder" of such
          Warrant) and will not be bound to recognize any equitable or other
          claim to or interest in such Warrant on the part of any other person
          and will not be liable for any registration of transfer of Warrants
          that are registered or to be registered in the name of a fiduciary or
          the nominee of a fiduciary.

     2.2  Transfer.  The Warrants (and the Warrant Shares) will be transferable
          --------
          only to the extent of, and in accordance with, Section 7 of the
          Warrant Purchase Agreement.

     2.3  Form of Warrant.  The Warrant Certificates will be executed on behalf
          ---------------
          of the Company by the Chairman of the Board of Directors of the
          Company (the "Board"), its President or one of its Vice Presidents and
          attested to by the Secretary of the Company or an Assistant Secretary.
          The signature of any of such officers on the Warrants may be manual or
          facsimile.

3.   Exchange of Warrants. Each Warrant may be exchanged at the option of the
     --------------------
     holder thereof for another Warrant or Warrants entitling the holder thereof
     to purchase a like aggregate number of Warrant Shares as the Warrant or
     Warrants surrendered then entitle such holder to purchase.  Any holder
     desiring to exchange a Warrant or Warrants will make such request in
     writing delivered to the Secretary of the Company and will surrender,
     properly endorsed, the Warrant or Warrants to be so exchanged at the office
     of the Secretary of the Company.  Thereupon, a new Warrant or Warrants, as
     the case may be, as so requested, will be delivered to the person entitled
     thereto.

4.   Term of Warrants; Exercise of Warrants.
     --------------------------------------

     4.1  Exercisability of Warrants.  The Warrants represented by this Warrant
          --------------------------
          Certificate are (***).

                                      -2-
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     4.2  Term.  THE WARRANTS EXPIRE AT THE EXPIRATION TIME.
          ----

     4.3  Exercise of Warrants.
          --------------------

          (a)  A Warrant that has become exercisable pursuant to Section 4.1 may
               be exercised prior to the Expiration Time upon surrender to the
               Company, in care of the Secretary of the Company, of the Warrant
               to be exercised, together with the duly completed and signed
               Election to Purchase in substantially the form attached hereto as

               Exhibit B (the "Election to Purchase"), and upon payment to the
               ---------
               Company of the Warrant Price for the number of Warrant Shares in
               respect of which such Warrant is then exercised.  Payment of the
               aggregate Warrant Price will be made by wire transfer of
               immediately available funds in accordance with written wire
               transfer instructions to be provided by the Company or by
               converting this Warrant Certificate, or any portion thereof
               pursuant to Section 4.2(b) ("Warrant Conversion").

          (b)  A Warrant may be exercised in a cashless manner (a "Cashless
               Exercise") with respect to a particular number of  Warrant Shares
               subject to the Warrant (the "Converted Warrant Shares") through
               Warrant Conversion by specifying such election in the Election to
               Purchase.  In such event, the Company will issue and cause to be
               delivered (without payment of any Warrant Price or any cash or
               other consideration) that number of Warrant Shares equal to the
               quotient obtained by dividing (1) the value of the Warrant (or
               the specified portion hereof) on the date of exercise, which
               value will be determined by subtracting (A) the aggregate Warrant
               Price of the Converted Warrant Shares immediately prior to the
               exercise of the Warrant from (B) the aggregate fair market value
               of the Converted Warrant Shares issuable upon exercise of the
               Warrant on the date of exercise, by (2) the fair market value of
               one Warrant Share on the date of exercise.  For purposes of this
               Section 3.2, fair market value of a Warrant Share as of a
               particular date will be the Closing Price on the Business Day
               immediately prior to the exercise of the applicable Warrant (or,
               if not publicly traded, the fair market value as determined in
               clause (B) of term "Fair Market Value").

          (c)  Upon such surrender of the Warrant and payment of the Warrant
               Price (or upon a Cashless Exercise), the Company will issue and
               cause to be delivered with all reasonable dispatch to or upon the
               written order of the holder and in such name or names as the
               holder may designate, a certificate or certificates for the
               number of full Warrant Shares so purchased upon the exercise of
               such Warrants, together with a check or cash in respect of any
               fraction of a share of Common Stock otherwise deliverable upon
               such exercise, as provided in Section 6.  Such certificate

                                      -3-
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               or certificates will be deemed to have been issued and any person
               so designated to be named therein will be deemed to have become a
               holder of record of such Warrant Shares as of the date of the
               surrender of such Warrants and payment of the Warrant Price;
               provided, however, that if, at the date of surrender of such
               --------  -------
               Warrant and payment of such Warrant Price, the transfer books for
               the Warrant Shares or other class of stock purchasable upon the
               exercise of such Warrant will be closed, the certificates for the
               Warrant Shares in respect of which such Warrant is then exercised
               will be issuable as of the date on which such books will next be
               opened (whether before or after the Expiration Time) and until
               such date the Company will be under no duty to deliver any
               certificate for such Warrant Shares; provided, further, that the
                                                    --------  -------
               transfer books, unless otherwise required by law, will not be
               closed at any one time for a period longer than twenty (20) days.

          (d)  The rights of purchase represented by the Warrant that have
               become exercisable pursuant to Section 4.1, will be exercisable
               at the election of the holders thereof, either in full or from
               time to time in part.  If a Warrant is exercised in respect of
               less than all of the Warrant Shares purchasable on such exercise
               at any time prior to the Expiration Time, a new Warrant
               evidencing the remaining Warrant Shares will be issued, and the
               Company will deliver the new Warrant pursuant to the provisions
               of this Section 4.2.

          (e)  Notwithstanding any other provision hereof, if an exercise of any
               portion of this Warrant is to be made in connection with a public
               offering of the Common Stock or a Business Combination, such
               exercise may at the election of the holder be conditioned upon
               the conclusion of such transaction, in which case such exercise
               will not be deemed to be effective until the conclusion of such
               transaction.

5.   Adjustment of Warrant Price and Number of Warrant Shares.  The number and
     --------------------------------------------------------
     kind of securities purchasable upon the exercise of each Warrant and the
     Warrant Price will be subject to adjustment from time to time as follows:

     5.1  Subdivisions, Combinations and Other Issuances.  If the Company will
          ----------------------------------------------
          at any time prior to the expiration of each Warrant subdivide the
          Common Stock, by split-up or otherwise, or combine the Common Stock,
          or issue additional shares of the Common Stock as a dividend with
          respect to any shares of the Common Stock, the number of Warrant
          Shares issuable on the exercise of the Warrant will forthwith be
          proportionately increased in the case of a subdivision or stock
          dividend, or proportionately decreased in the case of a combination.
          Appropriate adjustments will also be made to the Warrant Price, but
          the aggregate purchase price payable for the total number of Warrant
          Shares purchasable under the Warrant (as adjusted) will remain the
          same.  Any adjustment under this

                                      -4-
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          Section 5.1 will become effective at the close of business on the date
          the subdivision or combination becomes effective, or as of the record
          date of such dividend, or in the event that no record date is fixed,
          upon the making of such dividend.

     5.2  Recapitalization, Reclassification, Reorganization and Consolidation.
          --------------------------------------------------------------------
          In case of any recapitalization, reclassification, capital
          reorganization or change in the Common Stock of the Company (other
          than as a result of a subdivision, combination, or stock dividend
          provided for in Section 5.1), then, as a condition of such
          recapitalization, reclassification, reorganization or change, lawful
          provision will be made, and duly executed documents evidencing the
          same from the Company or its successor will be delivered to the
          holder, so that the holder will have the right at any time prior to
          the expiration of the Warrant to purchase, at a total price equal to
          that payable upon the exercise of the Warrant, the kind and amount of
          shares of stock and other securities and property receivable in
          connection with such recapitalization, reclassification,
          reorganization, or change by a holder of the same number of shares of
          Common Stock as were purchasable by the holder immediately prior to
          such recapitalization, reclassification, reorganization or change.  In
          any such case appropriate provisions will be made with respect to the
          rights and interest of the holder so that the provisions hereof will
          thereafter be applicable with respect to any shares of stock or other
          securities and property deliverable upon exercise hereof, and
          appropriate adjustments will be made to the Warrant Price payable
          hereunder, provided the aggregate purchase price will remain the same.

     5.3  Issuances Below $30.00 Per Share.  If the Company at any time prior to
          --------------------------------
          the Company's initial public offering of its Common Stock shall issue,
          or shall be deemed to issue (as provided in Section (E)(3)(b)(3) of
          Article IV of the Company's Amended and Restated Certificate of
          Incorporation), any shares of Common Stock (other than (i) "Excluded
          Stock," as defined in Article IV of the Company's Amended and Restated
          Certificate of Incorporation as of the date hereof, and (ii) the
          Series E Preferred Stock to be issued by the Corporation and subject
          to its Private Placement Investment Memorandum dated September 18,
          2000) at a price less than the Warrant Price then in effect, and if
          such issuance is not addressed by Sections 5.1, 5.2, or 5.5, the
          Warrant Price shall be reduced to reflect this lower price; provided,
                                                                      --------
          however, the aggregate number of Warrant Shares purchasable under the
          -------
          Warrant will remain the same.  Consideration other than cash shall be
          determined in accordance with Section (E)(3)(b)(2) of Article IV of
          the Company's Amended and Restated Certificate of Incorporation as of
          the date hereof.

     5.4  Notice of Adjustment.  When any adjustment is required to be made in
          --------------------
          the number or kind of shares purchasable upon exercise of each
          Warrant, or in the Warrant Price, the Company will promptly notify the
          holder of such event and of

                                      -5-
<PAGE>

          the number of shares of Common Stock or other securities or property
          thereafter purchasable upon exercise of the Warrant.

     5.5  Other Distributions.  In the event that the Company will, in respect
          -------------------
          of its outstanding shares of Common Stock, declare a distribution
          payable in securities of other persons, evidences of indebtedness
          issued by the Company or other persons, assets (excluding cash
          dividends) or options or rights not referred to in Sections 5.1 and
          5.2, then, in each such case for purposes of this Section 5.5, upon
          exercise of each Warrant the holder will be entitled to a
          proportionate share of any such distribution as though it were the
          holder of the number of shares of Common Stock of the Company
          underlying the Warrant as of the record date fixed for the
          determination of the holders of Common Stock of the Company entitled
          to receive such distribution.

     5.6  No Impairment.  The Company will not, by amendment of its Amended and
          -------------
          Restated Certificate of Incorporation or through any reorganization,
          recapitalization, transfer of assets, consolidation, merger,
          dissolution, issue or sale of securities or any other voluntary
          action, avoid or seek to avoid the observance or performance of any of
          the terms to be observed or performed hereunder by the Company, but
          will at all times in good faith assist in the carrying out of all the
          provisions of this Warrant Certificate and in the taking of all such
          action as may be necessary or appropriate in order to protect the
          exercise rights of the Holder against impairment.

     5.7  Minimum Adjustment.  The adjustments required by the preceding
          ------------------
          sections of this Section 5 shall be made whenever and as often as any
          specified event requiring an adjustment shall occur.  Subject to
          Section 6, adjustments of the Warrant Price or the number of shares of
          Common Stock issuable upon exercise of this Warrant shall be
          calculated to the nearest cent or to the nearest one hundredth of a
          share, as the case may be.  For the purpose of any adjustment, any
          specified event shall be deemed to have occurred at the close of
          business on the date of its occurrence.

     5.8  Adjustment to Warrant Certificate.  This Warrant Certificate need not
          ---------------------------------
          be changed because of any adjustment made pursuant to this Section 5,
          and Warrant Certificates issued after such adjustment may state the
          same Warrant Price and the same number of shares of Common Stock
          issuable upon exercise of the Warrants as are stated in the Warrant
          Certificates initially issued pursuant to this Warrant Agreement.  The
          Company, however, may at any time in its sole discretion make any
          change in the form of Warrant Certificate that it may deem appropriate
          to give effect to such adjustments and that does not affect the
          substance of the Warrant Certificate, and any Warrant Certificate
          thereafter issued or countersigned, whether in exchange or
          substitution for any outstanding Warrant Certificate or otherwise, may
          be in the form as so changed.

                                      -6-
<PAGE>

6.   Fractional Interests.  No fractional Warrant Shares or scrip will be issued
     --------------------
     upon the exercise of Warrants, but in lieu thereof the Company pay therefor
     in cash an amount equal to the product obtained by multiplying the Fair
     Market Value per Warrant Share on the Business Day immediately preceding
     the date of exercise of the Warrants times such fraction.  If more than one
     Warrant will be presented for exercise in full at the same time by the same
     holder, the number of full Warrant Shares that will be issuable upon the
     exercise thereof will be computed on the basis of the aggregate number of
     Warrant Shares purchasable on exercise of the Warrants so presented.

7.   Taxes.  The Company will pay any and all issue, transfer, documentary,
     -----
     stamp and other similar taxes that may be payable in respect of any issue
     or delivery of Warrant Shares upon the exercise of each Warrant; provided,
                                                                      --------
     however, that the Company will not be required to pay any tax or taxes that
     -------
     may be payable in respect of any transfer involved in the issue or delivery
     of any Warrant or certificates for Warrant Shares in a name other than that
     of the registered holder of such Warrant, and no such issue or delivery
     will be made unless and until the person requesting the issuance thereof
     will have paid to the Company the amount of such tax or will have
     established to the satisfaction of the Company that such tax has been paid.

8.   Reservation of Shares; Validity; Purchase and Cancellation of Warrants.
     ----------------------------------------------------------------------

     8.1  Reservation of Warrant Shares.  There have been reserved, and the
          -----------------------------
          Company will at all times reserve and keep available, free from
          preemptive rights, out of its authorized and unissued Common Stock,
          solely for the purpose of effecting the exercise of the Warrants, the
          number of shares of Common Stock that will from time to time be
          sufficient to provide for the exercise of the rights of purchase
          represented by the outstanding Warrants.  All Warrants surrendered in
          the exercise of the rights thereby evidenced will thereupon be
          cancelled by the Company and retired.  Promptly after the Expiration
          Time, the Secretary of the Company will certify to the Company the
          aggregate number of Warrants then outstanding, and thereafter no
          shares of Common Stock will be subject to reservation in respect of
          such Warrants.  The Company will from time to time, in accordance with
          the laws of the State of Delaware, use its commercially reasonable
          best efforts to increase the authorized amount of its Common Stock if
          at any time the number of shares of Common Stock remaining unissued
          will not be sufficient to permit the exercise of all the then
          outstanding Warrants.

     8.2  Valid Issuance.  Except for those restrictions set forth in the
          --------------
          Stockholder's Agreement, all shares of Common Stock or other
          securities issuable upon exercise of the Warrants will, upon issuance
          in accordance with the terms hereof, be validly issued, fully paid and
          nonassessable, free from all liens, charges, security interests and
          encumbrances created by the Company with respect to the issuance and
          delivery thereof and not subject to preemptive rights.

                                      -7-
<PAGE>

     8.3  Purchase of Warrants by the Company.  Any of the Company and its
          -----------------------------------
          Subsidiaries will have the right, except as limited by law, other
          agreements or herein, to purchase or otherwise acquire Warrants at
          such times, in such manner and for such consideration as it may deem
          appropriate.

     8.4  Cancellation of Warrants.  If any of the Company and its Subsidiaries
          ------------------------
          will purchase or otherwise acquire Warrants, the same will thereupon
          be cancelled by the Company and retired.  The Company will cancel any
          Warrant surrendered for exchange, substitution, transfer or exercise
          in whole or in part.

9.   Mutilated or Missing Warrants.  If any Warrant is mutilated, lost, stolen
     -----------------------------
     or destroyed and the Company receives evidence thereof reasonably
     satisfactory to it, the Company will issue and deliver in exchange and
     substitution for and upon cancellation of the mutilated Warrant, or in lieu
     of and substitution for the Warrant lost, stolen or destroyed, a new
     Warrant of like tenor and representing an equivalent right or interest.  An
     applicant for such a substitute Warrant will comply with such other
     reasonable requirements and pay such reasonable charges as the Company may
     prescribe.

10.  Rights as Stockholder.  Nothing contained in this Warrant Certificate or in
     ---------------------
     any of the Warrants will be construed as conferring upon the holders or
     their transferees the right to vote or to receive dividends or to consent
     or to receive notice as stockholders in respect of any meeting of
     stockholders for the election of directors of the Company or any other
     matter, or any rights whatsoever as stockholders of the Company.

11.  Notice to Holders.  At any time prior to the expiration of the Warrants and
     -----------------
     prior to their exercise, if any of the following events will occur:

     (a)  the Company will declare any dividend (or any other distribution) on
          Common Stock other than a cash dividend or will declare or authorize
          repurchase of in excess of 10% of the then outstanding shares of
          Common Stock; or

     (b)  the Company will authorize the granting to all holders of Common Stock
          of rights or warrants to subscribe for or purchase any shares of
          Common Stock or any Derivative Securities; or

     (c)  the Company will propose any capital reorganization, recapitalization,
          subdivision or reclassification of Common Stock (other than a
          subdivision or combination of the outstanding Common Stock, or a
          change in par value, or from par value to no par value or from no par
          value to par value), or any consolidation or merger to which the
          Company is a party for which approval of any stockholders of the
          Company will be required, or the sale, transfer or lease of all or
          substantially all of the assets of the Company, or any event described
          in Section 5; or

                                      -8-
<PAGE>

     (d)  the voluntary or involuntary dissolution, liquidation or winding up of
          the Company (other than in connection with a consolidation, merger, or
          sale of all or substantially all of its property, assets and business
          as an entirety) will be proposed;

     then the Company will give notice in writing of such event to the holders
     at least fifteen (15) days prior to the date fixed as a record date or the
     date of closing the transfer books for the determination of the
     stockholders entitled to such dividend, distribution, or subscription
     rights, or for the determination of stockholders entitled to vote on such
     proposed consolidation, merger, sale, transfer or lease of assets,
     dissolution, liquidation or winding up. No failure to give such notice or
     any defect therein or in the mailing thereof will affect the validity of
     the corporate action required to be specified in such notice.

12.  Notices.  All notices, requests and other communications with respect to
     -------
     the Warrants will be in writing. Communications may be made by telecopy or
     similar writing. Each communication will be given to the holder at the
     address in the Warrant Register, and to the Company at its offices in
     Oceanport, New Jersey, or at any other address as the holder or the
     Company, as the case may be, may specify for this purpose by notice to the
     other party. Each communication will be effective (a) if given by telecopy,
     when the telecopy is transmitted to the proper address and the receipt of
     the transmission is confirmed, (b) if given by mail, 72 hours after the
     communication is deposited in the mails properly addressed with first class
     postage prepaid, (c) if given by nationally-recognized overnight courier,
     on the next Business Day after the date when sent, or (d) if given by any
     other means, when delivered to the proper address and a written
     acknowledgement of delivery is received.

13.  No Waivers; Remedies; Specific Performance.
     ------------------------------------------

     13.1  No Waivers; Remedies.  Prior to the Expiration Time, no failure or
           --------------------
           delay by any holder in exercising any right, power or privilege with
           respect to the Warrants will operate as a waiver of the right, power
           or privilege. A single or partial exercise of any right, power or
           privilege will not preclude any other or further exercise of the
           right, power or privilege or the exercise of any other right, power
           or privilege. The rights and remedies provided in the Warrants will
           be cumulative and not exclusive of any rights or remedies provided by
           law.

     13.2  Specific Performance.  In view of the uniqueness of the Warrants, a
           --------------------
           holder would not have an adequate remedy at law for money damages in
           the event that any of the obligations arising under the Warrants is
           not performed in accordance with its terms, and the Company therefore
           agrees that the holder will be entitled to specific enforcement of
           the terms of the Warrants in addition to any other remedy to which
           they may be entitled, at law or in equity.

                                      -9-
<PAGE>

14.  Amendments, Etc.  No amendment, modification, termination, or waiver of any
     ---------------
     provision of this Warrant Certificate, and no consent to any departure from
     any provision of this Warrant Certificate, will be effective unless it will
     be in writing and signed and delivered by the Company and the holders of a
     majority of the outstanding Warrants (other than the Company), and then it
     will be effective only in the specific instance and for the specific
     purpose for which it is given. Any permitted transferee must agree in
     writing, as a condition of such transfer, to be bound by the terms and
     conditions of any amendment, modification, termination, or waiver of any
     provision of this Warrant Certificate which has been agreed to in writing
     by the transferor. The rights of the holder and the terms and provisions of
     this Warrant Certificate including, without limitation, the performance of
     the obligations of the Company hereunder, will not be affected in any
     manner whatsoever by the terms and provisions of any other agreement other
     than the Stockholder's Agreement, whether entered into prior to or after
     the date of this Warrant.

15.  Governing Law.  This Warrant Certificate will be governed by and construed
     -------------
     in accordance with the internal laws of the State of New York without
     regard to the principles of conflicts of law thereof.

16.  Severability of Provisions.  Any provision of this Warrant Certificate that
     --------------------------
     is prohibited or unenforceable in any jurisdiction shall, as to that
     jurisdiction, be ineffective to the extent of the prohibition or
     unenforceability without invalidating the remaining provisions of this
     Warrant Certificate or affecting the validity or enforceability of the
     provision in any other jurisdiction.

17.  Headings and References.  Headings in this Warrant Certificate are included
     -----------------------
     for the convenience of reference only and do not constitute a part of the
     Warrant for any other purpose. References to parties and sections in this
     Warrant Certificate are references to the parties or the sections of this
     Warrant Certificate, as the case may be, unless the context will require
     otherwise.

18.  Exclusive Jurisdiction.  Each of the Company and the holder, by acceptance
     ----------------------
     hereof, (a) agrees that any legal action with respect to this Warrant
     Certificate will be brought exclusively in the courts of the State of New
     York or of the United States of America, in each case within the County of
     New York, (b) accepts for itself and in respect of its property, generally
     and unconditionally, the jurisdiction of those courts, and (c) irrevocably
     waives any objection, including, without limitation, any objection to the
     laying of venue or based on the grounds of forum non conveniens, which it
                                                ----- --- ----------
     may now or hereafter have to the bringing of any legal action in those
     jurisdictions; provided, however, that any party may assert in a legal
                    --------  -------
     action in any other jurisdiction or venue each mandatory defense, third-
     party claim or similar claim that, if not so asserted in such legal action,
     may thereafter not be asserted by such party in an original legal action in
     the courts referred to in clause (a) above.

                                      -10-
<PAGE>

19.  Waiver of Jury Trial.  Each of the Company and the holder waives, by
     --------------------
     acceptance hereof, any right to a trial by jury in any legal action to
     enforce or defend any right under this Warrant Certificate or any
     amendment, instrument, document or agreement delivered, or which in the
     future may be delivered, in connection with this Warrant Certificate and
     agrees that any legal action will be tried before a court and not before a
     jury.

20.  Merger or Consolidation of the Company.  The Company will not merge or
     --------------------------------------
     consolidate with or into any other corporation or other entity where the
     Company is not the resulting or surviving corporation unless the entity
     resulting from such merger or consolidation, or its parent if the parent
     issues securities to the Company's security holders in such merger or
     consolidation, will expressly assume, by supplemental agreement, the due
     and punctual performance and observance of each and every covenant and
     condition of this Warrant Certificate to be performed and observed by the
     Company.

21.  Definitions.  For purposes of this Warrant Certificate, the following terms
     -----------
     have the following meanings:

     (a)  "Average Market Price" on any date means the average of the daily
          Closing Prices for the fifteen (15) consecutive Trading Days
          commencing twenty (20) Trading Days before such date.

     (b)  "Business Day" means any day excluding Saturday, Sunday and any day on
          which banking institutions located in the City of New York or Denver,
          Colorado are generally closed.

     (c)  "Business Combination" means, whether concluded or intended to be
          concluded in one transaction or series of transactions, each of the
          following:

          (1)  the merger or consolidation of any of the Company and its
               Subsidiaries with or into any person other than the Company or a
               wholly-owned Subsidiary of the Company;

          (2)  the transfer of all or substantially all of the assets of any of
               the Company and its Subsidiaries to any person or group other
               than the Company or a wholly-owned Subsidiary of the Company;

          (3)  an acquisition from any of the Company, its Subsidiaries and its
               stockholders of any shares of Common Stock or other Securities of
               the Company; or

          (4)  any tender offer (including a self-tender offer) or exchange
               offer, recapitalization, liquidation, dissolution or similar
               transaction involving any of the Company and its Subsidiaries.

                                      -11-
<PAGE>

     (d)  "Closing Price" means, as applied to any security on any date, the
          last reported sales price, regular way, per share of such security on
          such day, or if no such sale takes place on such day, the average of
          the closing bid and asked prices, regular way, in each case, as
          reported in the principal consolidated transaction reporting system
          with respect to securities listed or admitted to trading on the New
          York Stock Exchange or, if shares of such security are not listed or
          admitted to trading on the New York Stock Exchange, as reported in the
          principal consolidated transaction reporting system with respect to
          securities listed on the principal national securities exchange on
          which the shares of such security are listed or admitted to trading,
          or, if the shares of such security are not listed or admitted to
          trading on any national securities exchange, the last quoted sale
          price or, if not so quoted, the average of the high bid and low asked
          prices in the over-the-counter market, as reported by the National
          Association of Securities Dealers, Inc. Automated Quotations Systems
          ("NASDAQ") or, if not so reported, as reported by any similar
          interdealer system then in general use, or, if on any such date the
          shares of security are not quoted or reported by any such
          organization, the average of the closing bid and asked prices as
          furnished by a professional market maker making a market in the shares
          of stock selected by the Board.

     (e)  "Derivative Securities" means securities convertible into or
          exchangeable or exercisable for shares of Common Stock, rights or
          warrants to subscribe for or purchase shares of Common Stock, options
          for the purchase of, or calls, commitments or other claims of any
          character relating to, shares of Common Stock or any securities
          convertible into or exchangeable for any of the foregoing.

     (f)  "Expiration Time" means 5:00 p.m., New York time, on September 18,
          2005, (or, if not a Business Day, the next Business Day).

     (g)  "Fair Market Value" of any property will mean the fair market value
          thereof as determined in good faith by the Board; provided, however,
                                                            --------  -------
          that the value of any securities will be determined as follows:

               (A)  If publicly held or listed on an exchange or through the
                    NASDAQ National Market, the Average Market Price; and

               (B)  If not publicly held or so listed or publicly traded, the
                    value will be the fair market value thereof, as mutually
                    determined in good faith by the Board and the holders of a
                    majority of the Warrants and/or Warrant Shares purchasable
                    upon exercise thereof.

     (h)  "Stockholder's Agreement" means the Supplemental Stockholders'
          Agreement, dated as of the date hereof, by and between the Company,
          U.S. Telesource, Inc., and certain other persons.

                                      -12-
<PAGE>

     (i)  "Subsidiary" means (1) any corporation or other entity of which
          securities or other ownership interests having ordinary voting power
          to elect a majority of the board of directors or other persons
          performing similar functions are at the time directly or indirectly
          owned by the Company, or (2) a partnership or limited liability
          company in which the Company or a Subsidiary of the Company is, at the
          date of determination, a general or limited partner of such
          partnership or a member of such limited liability company, but only if
          the Company or its Subsidiary is entitled to receive more than fifty
          percent of the assets of such partnership or limited liability company
          upon its dissolution.

     (j)  "Trading Day" means, as applied to any class of stock, any day on
          which the New York Stock Exchange or, if shares of such stock are not
          listed or admitted to trading on the New York Stock Exchange, the
          principal national securities exchange on which the shares of such
          stock are listed or admitted for trading or, if the shares of such
          stock are not listed or admitted for trading on any national
          securities exchange, the NASDAQ or, if the shares of such stock are
          not included therein, any similar interdealer system then in general
          use in which the shares of such stock are included, is open for the
          trading of securities generally and with respect to which information
          regarding the sale of securities included therein, or with respect to
          which sales information is reported, is generally available.

                 [Remainder of Page Intentionally Left Blank]

                                      -13-
<PAGE>

     THIS WARRANT CERTIFICATE is executed and delivered by the Company on the
date set forth below in Oceanport, New Jersey.

Dated: September 18, 2000                    TELLIUM, INC.

                                             By: ____________________________

                                             Name: __________________________

                                             Title: _________________________

                                             Attested to:
                                             -----------

                                             By: ____________________________

                                             Name: __________________________

                                             Title: _________________________

                                      -1-
<PAGE>

                                   Exhibit A
                                   ---------

                                  ASSIGNMENT

                (To be signed only upon assignment of Warrant)

    FOR VALUE RECEIVED, the undersigned hereby sells, assigns and transfer unto

                        ______________________________
                                    (Name)

                        ______________________________

                        ______________________________
                                   (Address)

                        ______________________________
                           (Social Security Number)

the Warrant in the name of the undersigned and hereby appoints the Secretary of
the Company as the undersigned's attorney-in-fact to transfer said Warrant on
the books of the Company, with full power of substitution in the premises.

Date: __________, 20___

Signature of Registered Holder: _____________________________________________

Note: The above signature must correspond with the name as written upon the face
of this Warrant Certificate in every particular without alteration or
enlargement or any change whatever unless this Warrant has been assigned.

                                      -1-
<PAGE>

                                   Exhibit B
                                   ---------

                             ELECTION TO PURCHASE

Tellium, Inc.
2 Crescent Place
P.O. Box 901
Oceanport, NJ 07757-0901
Attn: Chief Financial Officer

     The undersigned hereby irrevocably elects to exercise the right of purchase
represented by the within Warrant for and to purchase thereunder, shares of the
stock provided for herein, and requests that certificates for such shares be
issued in the name of

                        ______________________________
                                    (Name)

                        ______________________________

                        ______________________________
                                   (Address)

                        ______________________________
                           (Social Security Number)

and, if said number of shares will not be all the shares purchasable thereunder,
that a new Warrant Certificate for the balance remaining of the shares
purchasable under the within Warrant Certificate be registered in the name of
the undersigned holder of this Warrant or his Assignee as below indicated and
delivered to the address stated below. By placing an X in the following blank,
the undersigned hereby elects to exercise the purchase right with respect to
__________ shares of such Common Stock through Warrant Conversion, as set forth
in Section 3 of the within Warrant.

Date: __________, 20___

Name of holder of this Warrant Certificate or Assignee: ________________________

Address: _______________________________________________________________________

Signature: _____________________________________________________________________

Note: The above signature must correspond with the name as written upon the face
of this Warrant Certificate in every particular without alteration or
enlargement or any change whatever unless this Warrant has been assigned.

                                      -1-<PAGE>

                                                                   Exhibit 10.18

Note: Redacted portions have been marked with (***). The redacted portions are
subject to a request for confidential treatment that has been filed with the
Securities and Exchange Commission.

                              WARRANT CERTIFICATE

                                 TELLIUM, INC.

                                "B" WARRANTS TO
                             PURCHASE COMMON STOCK

Certificate                                                      Certificate for
No. 1                                                     1,000,000 "B" Warrants

     THIS WARRANT CERTIFICATE CERTIFIES THAT U.S. TELESOURCE, INC., a Delaware
corporation ("U.S. Telesource"), or its registered assigns, is the registered
holder of the number of "B" Warrants (the "Warrants") set forth above which were
sold and granted to U.S. Telesource pursuant to the Warrant Purchase Agreement,
dated as of the date hereof, between U.S. Telesource and TELLIUM, INC., a
Delaware corporation (the "Company").  Each Warrant entitles the holder thereof
to subscribe for and purchase one fully paid and nonassessable share of common
stock, par value $.001 per share (the "Common Stock") (as adjusted pursuant to
Section 5, a "Share") of the Company, at any time and from time to time after
the date such Warrant becomes exercisable pursuant to Section 4.1 and prior to
the Expiration Time, at the purchase price of $30.00 per share (as such price
may be adjusted pursuant to Section 5, the "Warrant Price"), subject to the
provisions and upon the terms and conditions hereinafter set forth. Terms not
otherwise defined herein have the meanings stated in Section 24.

        THE SECURITIES REPRESENTED BY THIS CERTIFICATE HAVE BEEN
        ACQUIRED FOR INVESTMENT AND HAVE NOT BEEN REGISTERED UNDER THE
        SECURITIES ACT OF 1933. THESE SECURITIES MAY NOT BE SOLD OR
        TRANSFERRED IN THE ABSENCE OF SUCH REGISTRATION OR AN
        EXEMPTION THEREFROM UNDER SAID ACT. ADDITIONALLY, THE TRANSFER
        OF THESE SECURITIES IS SUBJECT TO THE CONDITIONS SPECIFIED IN
        SECTION 7 OF THE WARRANT PURCHASE AGREEMENT, AND NO TRANSFER
        OF THESE SECURITIES SHALL BE VALID OR EFFECTIVE UNTIL SUCH
        CONDITIONS HAVE BEEN FULFILLED. UPON THE FULFILLMENT OF
        CERTAIN SUCH CONDITIONS, THE SECRETARY OF TELLIUM, INC. HAS
        AGREED TO DELIVER TO THE HOLDER HEREOF A NEW CERTIFICATE, NOT
        BEARING THIS LEGEND, FOR THE SECURITIES REPRESENTED HEREBY
        REGISTERED IN THE NAME OF THE HOLDER HEREOF. COPIES OF SUCH
        AGREEMENT MAY BE OBTAINED AT NO COST BY WRITTEN REQUEST MADE
        BY THE HOLDER OF RECORD OF THIS CERTIFICATE TO THE SECRETARY
        OF TELLIUM, INC.
<PAGE>

1.   Vesting of Warrants.
     -------------------

     Pursuant to the Warrant Purchase Agreement, the Company sold and granted
the Warrants to U.S. Telesource.  Each Warrant is fully vested, shall be subject
to adjustment pursuant to Section 5, and shall become exercisable as set forth
in Section 4.

2.   Transferability of Warrants.
     ---------------------------

     2.1  Warrant Register and Registration.  The Secretary of the Company will
          ---------------------------------
          keep or cause to be kept at the office of the Company books for the
          registration and transfer (the "Warrant Register") of this Warrant
          Certificate and any other Warrant certificate issued hereunder
          (collectively, including the initial Warrant, the "Warrants").  The
          Warrant Certificates will be numbered and will be registered in the
          Warrant Register as they are issued.  The Company and the Secretary of
          the Company will be entitled to treat a person as the owner in fact
          for all purposes of each Warrant registered in such person's name
          (each registered owner is herein referred to as a "holder" of such
          Warrant) and will not be bound to recognize any equitable or other
          claim to or interest in such Warrant on the part of any other person
          and will not be liable for any registration of transfer of Warrants
          that are registered or to be registered in the name of a fiduciary or
          the nominee of a fiduciary.

     2.2  Transfer.  The Warrants (and the Warrant Shares) will be transferable
          --------
          only to the extent of, and in accordance with, Section 7 of the
          Warrant Purchase Agreement.

     2.3  Form of Warrant.  The Warrant Certificates will be executed on behalf
          ---------------
          of the Company by the Chairman of the Board of Directors of the
          Company (the "Board"), its President or one of its Vice Presidents and
          attested to by the Secretary of the Company or an Assistant Secretary.
          The signature of any of such officers on the Warrants may be manual or
          facsimile.

3.   Exchange of Warrants. Each Warrant may be exchanged at the option of the
     --------------------
     holder thereof for another Warrant or Warrants entitling the holder thereof
     to purchase a like aggregate number of Warrant Shares as the Warrant or
     Warrants surrendered then entitle such holder to purchase.  Any holder
     desiring to exchange a Warrant or Warrants will make such request in
     writing delivered to the Secretary of the Company and will surrender,
     properly endorsed, the Warrant or Warrants to be so exchanged at the office
     of the Secretary of the Company.  Thereupon, a new Warrant or Warrants, as
     the case may be, as so requested, will be delivered to the person entitled
     thereto.

                                      -2-
<PAGE>

4.   Term of Warrants; Exercise of Warrants.
     --------------------------------------

     4.1  Exercisability of Warrants.  The Warrants represented by this Warrant
          --------------------------
          Certificate are exercisable in whole or in part in accordance with the
          following:

          (a)  If Qwest has paid (***) pursuant to the Procurement Agreement,
               (***) Warrants are fully exercisable (it being understood and
               agreed that this Section 4.1(a) shall have been satisfied if
               Qwest has made payments and Deemed Payments to the Company
               aggregating such (***). "Deemed Payments" shall mean the
               aggregate purchase order amounts which are contained in valid and
               effective purchase orders (A) issued under Section 7.1 of the
               Procurement Agreement, (B) confirmed and accepted by the Company
               under Section 7.2 of the Procurement Agreement, and (C)
               containing stated delivery dates in case of the purchase orders
               under Section 7.1(a)(i) and agreed upon delivery dates in case of
               purchase orders under Section 7.1(a)(ii) (as postponed, suspended
               or amended from time to time pursuant to the Procurement
               Agreement) for which the Company has not satisfied its delivery
               obligations in circumstances in which the Company failed to use
               commercially reasonable efforts to meet such delivery dates.

          (b)  Notwithstanding the foregoing, the Warrants shall become
               exercisable with respect to any Warrant Shares which have not
               become exercisable prior to the (***) of the date hereof upon
               such anniversary.

          The Company shall keep a reasonably detailed record of all Qwest
          payments pursuant to the Procurement Agreement and receipt of all
          purchase orders, and shall furnish Qwest with a copy of such record
          bi-annually, within ten days after end of each six-month period;
          provided, however, the Company will provide Qwest with interim monthly
          --------  -------
          reports upon Qwest's written request.  Such record will contain, at a
          minimum, a listing of purchase orders, items purchased, date of
          delivery, name of purchaser, price paid by item and date purchased.

     4.2  Term.  THE WARRANTS EXPIRE AT THE EXPIRATION TIME.
          ----

     4.3  Exercise of Warrants.
          --------------------

          (a)  A Warrant that has become exercisable pursuant to Section 4.1 may
               be exercised prior to the Expiration Time upon surrender to the
               Company, in care of the Secretary of the Company, of the Warrant
               to be exercised, together with the duly completed and signed
               Election to Purchase in substantially the form attached hereto as
               Exhibit B (the "Election to Purchase"), and upon payment to the
               ---------
               Company of the Warrant Price for the number of Warrant Shares in
               respect of which such Warrant is then

                                      -3-
<PAGE>

               exercised. Payment of the aggregate Warrant Price will be made by
               wire transfer of immediately available funds in accordance with
               written wire transfer instructions to be provided by the Company
               or by converting this Warrant Certificate, or any portion thereof
               pursuant to Section 4.2(b) ("Warrant Conversion").

          (b)  A Warrant may be exercised in a cashless manner (a "Cashless
               Exercise") with respect to a particular number of  Warrant Shares
               subject to the Warrant (the "Converted Warrant Shares") through
               Warrant Conversion by specifying such election in the Election to
               Purchase.  In such event, the Company will issue and cause to be
               delivered (without payment of any Warrant Price or any cash or
               other consideration) that number of Warrant Shares equal to the
               quotient obtained by dividing (1) the value of the Warrant (or
               the specified portion hereof) on the date of exercise, which
               value will be determined by subtracting (A) the aggregate Warrant
               Price of the Converted Warrant Shares immediately prior to the
               exercise of the Warrant from (B) the aggregate fair market value
               of the Converted Warrant Shares issuable upon exercise of the
               Warrant on the date of exercise, by (2) the fair market value of
               one Warrant Share on the date of exercise.  For purposes of this
               Section 3.2, fair market value of a Warrant Share as of a
               particular date will be the Closing Price on the Business Day
               immediately prior to the exercise of the applicable Warrant (or,
               if not publicly traded, the fair market value as determined in
               clause (B) of the term "Fair Market Value".

          (c)  Upon such surrender of the Warrant and payment of the Warrant
               Price (or upon a Cashless Exercise), the Company will issue and
               cause to be delivered with all reasonable dispatch to or upon the
               written order of the holder and in such name or names as the
               holder may designate, a certificate or certificates for the
               number of full Warrant Shares so purchased upon the exercise of
               such Warrants, together with a check or cash in respect of any
               fraction of a share of Common Stock otherwise deliverable upon
               such exercise, as provided in Section 6.  Such certificate or
               certificates will be deemed to have been issued and any person so
               designated to be named therein will be deemed to have become a
               holder of record of such Warrant Shares as of the date of the
               surrender of such Warrants and payment of the Warrant Price;
               provided, however, that if, at the date of surrender of such
               --------  -------
               Warrant and payment of such Warrant Price, the transfer books for
               the Warrant Shares or other class of stock purchasable upon the
               exercise of such Warrant will be closed, the certificates for the
               Warrant Shares in respect of which such Warrant is then exercised
               will be issuable as of the date on which such books will next be
               opened (whether before or after the Expiration Time) and until

                                      -4-
<PAGE>

               such date the Company will be under no duty to deliver any
               certificate for such Warrant Shares; provided, further, that the
                                                    --------  -------
               transfer books, unless otherwise required by law, will not be
               closed at any one time for a period longer than twenty (20) days.

          (d)  The rights of purchase represented by the Warrant that have
               become exercisable pursuant to Section 4.1, will be exercisable
               at the election of the holders thereof, either in full or from
               time to time in part.  If a Warrant is exercised in respect of
               less than all of the Warrant Shares purchasable on such exercise
               at any time prior to the Expiration Time, a new Warrant
               evidencing the remaining Warrant Shares will be issued, and the
               Company will deliver the new Warrant pursuant to the provisions
               of this Section 4.2.

          (e)  Notwithstanding any other provision hereof, if an exercise of any
               portion of this Warrant is to be made in connection with a public
               offering of the Common Stock or a Business Combination, such
               exercise may at the election of the holder be conditioned upon
               the conclusion of such transaction, in which case such exercise
               will not be deemed to be effective until the conclusion of such
               transaction.

5.   Adjustment of Warrant Price and Number of Warrant Shares.  The number and
     --------------------------------------------------------
     kind of securities purchasable upon the exercise of each Warrant and the
     Warrant Price will be subject to adjustment from time to time as follows:

     5.1  Subdivisions, Combinations and Other Issuances.  If the Company will
          ----------------------------------------------
          at any time prior to the expiration of each Warrant subdivide the
          Common Stock, by split-up or otherwise, or combine the Common Stock,
          or issue additional shares of the Common Stock as a dividend with
          respect to any shares of the Common Stock, the number of Warrant
          Shares issuable on the exercise of the Warrant will forthwith be
          proportionately increased in the case of a subdivision or stock
          dividend, or proportionately decreased in the case of a combination.
          Appropriate adjustments will also be made to the Warrant Price, but
          the aggregate purchase price payable for the total number of Warrant
          Shares purchasable under the Warrant (as adjusted) will remain the
          same.  Any adjustment under this Section 5.1 will become effective at
          the close of business on the date the subdivision or combination
          becomes effective, or as of the record date of such dividend, or in
          the event that no record date is fixed, upon the making of such
          dividend.

     5.2  Recapitalization, Reclassification, Reorganization and Consolidation.
          --------------------------------------------------------------------
          In case of any recapitalization, reclassification, capital
          reorganization or change in the Common Stock of the Company (other
          than as a result of a subdivision, combination, or stock dividend
          provided for in Section 5.1), then, as a condition of such
          recapitalization, reclassification, reorganization or change, lawful

                                      -5-
<PAGE>

          provision will be made, and duly executed documents evidencing the
          same from the Company or its successor will be delivered to the
          holder, so that the holder will have the right at any time prior to
          the expiration of each Warrant to purchase, at a total price equal to
          that payable upon the exercise of this Warrant, the kind and amount of
          shares of stock and other securities and property receivable in
          connection with such recapitalization, reclassification,
          reorganization, or change by a holder of the same number of shares of
          Common Stock as were purchasable by the holder immediately prior to
          such recapitalization, reclassification, reorganization or change.  In
          any such case appropriate provisions will be made with respect to the
          rights and interest of the holder so that the provisions hereof will
          thereafter be applicable with respect to any shares of stock or other
          securities and property deliverable upon exercise hereof, and
          appropriate adjustments will be made to the Warrant Price payable
          hereunder, provided the aggregate purchase price will remain the same.

     5.3  Issuances Below $30.00 Per Share.  If the Company at any time prior to
          --------------------------------
          the Company's initial public offering of its Common Stock shall issue,
          or shall be deemed to issue (as provided in Section (E)(3)(b)(3) of
          Article IV of the Company's Amended and Restated Certificate of
          Incorporation), any shares of Common Stock (other than (i) "Excluded
          Stock," as defined in Article IV of the Company's Amended and Restated
          Certificate of Incorporation as of the date hereof, and (ii) the
          Series E Preferred Stock to be issued by the Corporation and subject
          to its Private Placement Investment Memorandum dated September 18,
          2000) at a price less than the Warrant Price then in effect, and if
          such issuance is not addressed by Sections 5.1, 5.2, or 5.5, the
          Warrant Price shall be reduced to reflect this lower price; provided,
                                                                      --------
          however, the aggregate number of Warrant Shares purchasable under the
          -------
          Warrant will remain the same.  Consideration other than cash shall be
          determined in accordance with Section (E)(3)(b)(2) of Article IV of
          the Company's Amended and Restated Certificate of Incorporation as of
          the date hereof.

     5.4  Notice of Adjustment.  When any adjustment is required to be made in
          --------------------
          the number or kind of shares purchasable upon exercise of each
          Warrant, or in the Warrant Price, the Company will promptly notify the
          holder of such event and of the number of shares of Common Stock or
          other securities or property thereafter purchasable upon exercise of
          the Warrant.

     5.5  Other Distributions.  In the event that the Company will, in respect
          -------------------
          of its outstanding shares of Common Stock, declare a distribution
          payable in securities of other persons, evidences of indebtedness
          issued by the Company or other persons, assets (excluding cash
          dividends) or options or rights not referred to in Sections 5.1 and
          5.2, then, in each such case for purposes of this Section 5.5, upon
          exercise of each Warrant the holder will be entitled to a
          proportionate share of any such distribution as though it were the
          holder of the number of shares of

                                      -6-
<PAGE>

          Common Stock of the Company underlying the Warrant as of the record
          date fixed for the determination of the holders of Common Stock of the
          Company entitled to receive such distribution.

     5.6  No Impairment.  The Company will not, by amendment of its Amended and
          -------------
          Restated Certificate of Incorporation or through any reorganization,
          recapitalization, transfer of assets, consolidation, merger,
          dissolution, issue or sale of securities or any other voluntary
          action, avoid or seek to avoid the observance or performance of any of
          the terms to be observed or performed hereunder by the Company, but
          will at all times in good faith assist in the carrying out of all the
          provisions of this Warrant Certificate and in the taking of all such
          action as may be necessary or appropriate in order to protect the
          exercise rights of the Holder against impairment.

     5.7  Minimum Adjustment.  The adjustments required by the preceding
          ------------------
          sections of this Section 5 shall be made whenever and as often as any
          specified event requiring an adjustment shall occur.  Subject to
          Section 6, adjustments of the Warrant Price or the number of shares of
          Common Stock issuable upon exercise of this Warrant shall be
          calculated to the nearest cent or to the nearest one hundredth of a
          share, as the case may be.  For the purpose of any adjustment, any
          specified event shall be deemed to have occurred at the close of
          business on the date of its occurrence.

     5.8  Adjustment to Warrant Certificate.  This Warrant Certificate need not
          ---------------------------------
          be changed because of any adjustment made pursuant to this Section 5,
          and Warrant Certificates issued after such adjustment may state the
          same Warrant Price and the same number of shares of Common Stock
          issuable upon exercise of the Warrants as are stated in the Warrant
          Certificates initially issued pursuant to this Warrant Agreement.  The
          Company, however, may at any time in its sole discretion make any
          change in the form of Warrant Certificate that it may deem appropriate
          to give effect to such adjustments and that does not affect the
          substance of the Warrant Certificate, and any Warrant Certificate
          thereafter issued or countersigned, whether in exchange or
          substitution for any outstanding Warrant Certificate or otherwise, may
          be in the form as so changed.

6.   Fractional Interests.  No fractional Warrant Shares or scrip will be issued
     --------------------
     upon the exercise of Warrants, but in lieu thereof the Company pay therefor
     in cash an amount equal to the product obtained by multiplying the Fair
     Market Value per Warrant Share on the Business Day immediately preceding
     the date of exercise of the Warrants times such fraction.  If more than one
     Warrant will be presented for exercise in full at the same time by the same
     holder, the number of full Warrant Shares that will be issuable upon the
     exercise thereof will be computed on the basis of the aggregate number of
     Warrant Shares purchasable on exercise of the Warrants so presented.

                                      -7-
<PAGE>

7.   Taxes.  The Company will pay any and all issue, transfer, documentary,
     -----
     stamp and other similar taxes that may be payable in respect of any issue
     or delivery of Warrant Shares upon the exercise of each Warrant; provided,
                                                                      --------
     however, that the Company will not be required to pay any tax or taxes that
     -------
     may be payable in respect of any transfer involved in the issue or delivery
     of any Warrant or certificates for Warrant Shares in a name other than that
     of the registered holder of such Warrant, and no such issue or delivery
     will be made unless and until the person requesting the issuance thereof
     will have paid to the Company the amount of such tax or will have
     established to the satisfaction of the Company that such tax has been paid.

8.   Reservation of Shares; Validity; Purchase and Cancellation of Warrants.
     ----------------------------------------------------------------------

     8.1  Reservation of Warrant Shares.  There have been reserved, and the
          -----------------------------
          Company will at all times reserve and keep available, free from
          preemptive rights, out of its authorized and unissued Common Stock,
          solely for the purpose of effecting the exercise of the Warrants, the
          number of shares of Common Stock that will from time to time be
          sufficient to provide for the exercise of the rights of purchase
          represented by the outstanding Warrants.  All Warrants surrendered in
          the exercise of the rights thereby evidenced will thereupon be
          cancelled by the Company and retired.  Promptly after the Expiration
          Time, the Secretary of the Company will certify to the Company the
          aggregate number of Warrants then outstanding, and thereafter no
          shares of Common Stock will be subject to reservation in respect of
          such Warrants.  The Company will from time to time, in accordance with
          the laws of the State of Delaware, use its commercially reasonable
          best efforts to increase the authorized amount of its Common Stock if
          at any time the number of shares of Common Stock remaining unissued
          will not be sufficient to permit the exercise of all the then
          outstanding Warrants.

     8.2  Valid Issuance.  Except for those restrictions set forth in the
          --------------
          Stockholder's Agreement, all shares of Common Stock or other
          securities issuable upon exercise of the Warrants will, upon issuance
          in accordance with the terms hereof, be validly issued, fully paid and
          nonassessable, free from all liens, charges, security interests and
          encumbrances created by the Company with respect to the issuance and
          delivery thereof and not subject to preemptive rights.

     8.3  Purchase of Warrants by the Company.  Any of the Company and its
          -----------------------------------
          Subsidiaries will have the right, except as limited by law, other
          agreements or herein, to purchase or otherwise acquire Warrants at
          such times, in such manner and for such consideration as it may deem
          appropriate.

     8.4  Cancellation of Warrants.  If any of the Company and its Subsidiaries
          ------------------------
          will purchase or otherwise acquire Warrants, the same will thereupon
          be cancelled by the Company and retired.  The Company will cancel any
          Warrant surrendered for exchange, substitution, transfer or exercise
          in whole or in part.

                                      -8-
<PAGE>

9.   Mutilated or Missing Warrants.  If any Warrant is mutilated, lost, stolen
     -----------------------------
     or destroyed and the Company receives evidence thereof reasonably
     satisfactory to it, the Company will issue and deliver in exchange and
     substitution for and upon cancellation of the mutilated Warrant, or in lieu
     of and substitution for the Warrant lost, stolen or destroyed, a new
     Warrant of like tenor and representing an equivalent right or interest.  An
     applicant for such a substitute Warrant will comply with such other
     reasonable requirements and pay such reasonable charges as the Company may
     prescribe.

10.  Rights as Stockholder.  Nothing contained in this Warrant Certificate or in
     ---------------------
     any of the Warrants will be construed as conferring upon the holders or
     their transferees the right to vote or to receive dividends or to consent
     or to receive notice as stockholders in respect of any meeting of
     stockholders for the election of directors of the Company or any other
     matter, or any rights whatsoever as stockholders of the Company.

11.  Notice to Holders.  At any time prior to the expiration of the Warrants and
     -----------------
     prior to their exercise, if any of the following events will occur:

     (a)  the Company will declare any dividend (or any other distribution) on
          Common Stock other than a cash dividend or will declare or authorize
          repurchase of in excess of 10% of the then outstanding shares of
          Common Stock; or

     (b)  the Company will authorize the granting to all holders of Common Stock
          of rights or warrants to subscribe for or purchase any shares of
          Common Stock or any Derivative Securities; or

     (c)  the Company will propose any capital reorganization, recapitalization,
          subdivision or reclassification of Common Stock (other than a
          subdivision or combination of the outstanding Common Stock, or a
          change in par value, or from par value to no par value or from no par
          value to par value), or any consolidation or merger to which the
          Company is a party for which approval of any stockholders of the
          Company will be required, or the sale, transfer or lease of all or
          substantially all of the assets of the Company, or any event described
          in Section 5; or

     (d)  the voluntary or involuntary dissolution, liquidation or winding up of
          the Company (other than in connection with a consolidation, merger, or
          sale of all or substantially all of its property, assets and business
          as an entirety) will be proposed;

     then the Company will give notice in writing of such event to the holders
     at least fifteen (15) days prior to the date fixed as a record date or the
     date of closing the transfer books for the determination of the
     stockholders entitled to such dividend, distribution, or subscription
     rights, or for the determination of stockholders entitled to vote on such
     proposed consolidation, merger, sale, transfer or lease of assets,
     dissolution, liquidation or winding up.  No failure to give such notice or
     any defect therein or in the mailing

                                      -9-
<PAGE>

     thereof will affect the validity of the corporate action required to be
     specified in such notice.

12.  Notices.  All notices, requests and other communications with respect to
     -------
     the Warrants will be in writing.  Communications may be made by telecopy or
     similar writing.  Each communication will be given to the holder at the
     address in the Warrant Register, and to the Company at its offices in
     Oceanport, New Jersey, or at any other address as the holder or the
     Company, as the case may be, may specify for this purpose by notice to the
     other party.  Each communication will be effective (a) if given by
     telecopy, when the telecopy is transmitted to the proper address and the
     receipt of the transmission is confirmed, (b) if given by mail, 72 hours
     after the communication is deposited in the mails properly addressed with
     first class postage prepaid, (c) if given by nationally-recognized
     overnight courier, on the next Business Day after the date when sent, or
     (d) if given by any other means, when delivered to the proper address and a
     written acknowledgement of delivery is received.

13.  No Waivers; Remedies; Specific Performance.
     ------------------------------------------

     13.1  No Waivers; Remedies.  Prior to the Expiration Time, no failure or
           --------------------
           delay by any holder in exercising any right, power or privilege with
           respect to the Warrants will operate as a waiver of the right, power
           or privilege. A single or partial exercise of any right, power or
           privilege will not preclude any other or further exercise of the
           right, power or privilege or the exercise of any other right, power
           or privilege. The rights and remedies provided in the Warrants will
           be cumulative and not exclusive of any rights or remedies provided by
           law.

     13.2  Specific Performance.  In view of the uniqueness of the Warrants, a
           --------------------
           holder would not have an adequate remedy at law for money damages in
           the event that any of the obligations arising under the Warrants is
           not performed in accordance with its terms, and the Company therefore
           agrees that the holder will be entitled to specific enforcement of
           the terms of the Warrants in addition to any other remedy to which
           they may be entitled, at law or in equity.

14.  Amendments, Etc.  No amendment, modification, termination, or waiver of any
     ---------------
     provision of this Warrant Certificate, and no consent to any departure from
     any provision of this Warrant Certificate, will be effective unless it will
     be in writing and signed and delivered by the Company and the holders of a
     majority of the outstanding Warrants (other than the Company), and then it
     will be effective only in the specific instance and for the specific
     purpose for which it is given.  Any permitted transferee must agree in
     writing, as a condition of such transfer, to be bound by the terms and
     conditions of any amendment, modification, termination, or waiver of any
     provision of this Warrant Certificate which has been agreed to in writing
     by the transferor.  The rights of the holder and the terms and provisions
     of this Warrant Certificate including, without limitation, the performance
     of the obligations of the Company hereunder, will not be affected in any

                                      -10-
<PAGE>

     manner whatsoever by the terms and provisions of any other agreement other
     than the Stockholder's Agreement, whether entered into prior to or after
     the date of this Warrant Certificate.

15.  Governing Law.  This Warrant Certificate will be governed by and construed
     -------------
     in accordance with the internal laws of the State of New York without
     regard to the principles of conflicts of law thereof.

16.  Severability of Provisions.  Any provision of this Warrant Certificate that
     --------------------------
     is prohibited or unenforceable in any jurisdiction shall, as to  that
     jurisdiction, be ineffective to the extent of the prohibition or
     unenforceability without invalidating the remaining provisions of this
     Warrant Certificate or affecting the validity or enforceability of the
     provision in any other jurisdiction.

17.  Headings and References.  Headings in this Warrant Certificate are included
     -----------------------
     for the convenience of reference only and do not constitute a part of the
     Warrants for any other purpose.  References to parties and sections in this
     Warrant Certificate are references to the parties or the sections of this
     Warrant Certificate, as the case may be, unless the context will require
     otherwise.

18.  Exclusive Jurisdiction.  Each of the Company and the holder, by acceptance
     ----------------------
     hereof, (a) agrees that any legal action with respect to this Warrant
     Certificate will be brought exclusively in the courts of the State of New
     York or of the United States of America, in each case within the County of
     New York, (b) accepts for itself and in respect of its property, generally
     and unconditionally, the jurisdiction of those courts, and (c) irrevocably
     waives any objection, including, without limitation, any objection to the
     laying of venue or based on the grounds of forum non conveniens, which it
                                                ----- --- ----------
     may now or hereafter have to the bringing of any legal action in those
     jurisdictions; provided, however, that any party may assert in a legal
                    --------  -------
     action in any other jurisdiction or venue each mandatory defense, third-
     party claim or similar claim that, if not so asserted in such legal action,
     may thereafter not be asserted by such party in an original legal action in
     the courts referred to in clause (a) above.

19.  Waiver of Jury Trial.  Each of the Company and the holder waives, by
     --------------------
     acceptance hereof, any right to a trial by jury in any legal action to
     enforce or defend any right under this Warrant Certificate or any
     amendment, instrument, document or agreement delivered, or which in the
     future may be delivered, in connection with this Warrant Certificate and
     agrees that any legal action will be tried before a court and not before a
     jury.

20.  Merger or Consolidation of the Company.  The Company will not merge or
     --------------------------------------
     consolidate with or into any other corporation or other entity where the
     Company is not the resulting or surviving corporation unless the entity
     resulting from such merger or consolidation, or its parent if the parent
     issues securities to the Company's security

                                      -11-
<PAGE>

     holders in such merger of consolidation, will expressly assume, by
     supplemental agreement, the due and punctual performance and observance of
     each and every covenant and condition of this Warrant Certificate to be
     performed and observed by the Company.

21.  Definitions.  For purposes of this Warrant Certificate, the following terms
     -----------
     have the following meanings:

     (a)  "Average Market Price" on any date means the average of the daily
          Closing Prices for the fifteen (15) consecutive Trading Days
          commencing twenty (20) Trading Days before such date.

     (b)  "Business Day" means any day excluding Saturday, Sunday and any day on
          which banking institutions located in the City of New York or Denver,
          Colorado are generally closed.

     (c)  "Business Combination" means, whether concluded or intended to be
          concluded in one transaction or series of transactions, each of the
          following:

          (1)  the merger or consolidation of any of the Company and its
               Subsidiaries with or into any person other than the Company or a
               wholly-owned Subsidiary of the Company;

          (2)  the transfer of all or substantially all of the assets of any of
               the Company and its Subsidiaries to any person or group other
               than the Company or a wholly-owned Subsidiary of the Company;

          (3)  an acquisition from any of the Company, its Subsidiaries and its
               stockholders of any shares of Common Stock or other Securities of
               the Company; or

          (4)  any tender offer (including a self-tender offer) or exchange
               offer, recapitalization, liquidation, dissolution or similar
               transaction involving any of the Company and its Subsidiaries.

     (d)  "Closing Price" means, as applied to any security on any date, the
          last reported sales price, regular way, per share of such security on
          such day, or if no such sale takes place on such day, the average of
          the closing bid and asked prices, regular way, in each case, as
          reported in the principal consolidated transaction reporting system
          with respect to securities listed or admitted to trading on the New
          York Stock Exchange or, if shares of such security are not listed or
          admitted to trading on the New York Stock Exchange, as reported in the
          principal consolidated transaction reporting system with respect to
          securities listed on the principal national securities exchange on
          which the shares of such security are listed or admitted to trading,
          or, if the shares of such security are not listed or admitted to
          trading on any national securities exchange, the last quoted sale
          price or, if not so

                                      -12-
<PAGE>

          quoted, the average of the high bid and low asked prices in the over-
          the-counter market, as reported by the National Association of
          Securities Dealers, Inc. Automated Quotations Systems ("NASDAQ") or,
          if not so reported, as reported by any similar interdealer system then
          in general use, or, if on any such date the shares of security are not
          quoted or reported by any such organization, the average of the
          closing bid and asked prices as furnished by a professional market
          maker making a market in the shares of stock selected by the Board.

     (e)  "Derivative Securities" means securities convertible into or
          exchangeable or exercisable for shares of Common Stock, rights or
          warrants to subscribe for or purchase shares of Common Stock, options
          for the purchase of, or calls, commitments or other claims of any
          character relating to, shares of Common Stock or any securities
          convertible into or exchangeable for any of the foregoing.

     (f)  "Expiration Time" means 5:00 p.m., New York time, on the later of (i)
          September 18, 2005 or (ii) six (6) months after the last day the
          Warrant becomes exercisable with respect to any of the underlying
          Warrant Shares, or in either case if not a Business Day, the next
          Business Day.

     (g)  "Fair Market Value" of any property will mean the fair market value
          thereof as determined in good faith by the Board; provided, however,
                                                            --------  -------
          that the value of any securities will be determined as follows:

               (A)  If publicly held or listed on an exchange or through the
                    NASDAQ National Market, the Average Market Price; and

               (B)  If not publicly held or so listed or publicly traded, the
                    value will be the fair market value thereof, as mutually
                    determined in good faith by the Board and the holders of a
                    majority of the Warrants and/or Warrant Shares purchasable
                    upon exercise thereof.

     (h)  "Procurement Agreement" means the Procurement Agreement, dated as of
          the date hereof, by and between Qwest and the Company.

     (i)  "Qwest" means Qwest Communications Corporation.

     (j)  "Stockholder's Agreement" means the Supplemental Stockholders'
          Agreement, dated as of the date hereof, by and between the Company,
          U.S. Telesource, Inc., and certain other persons.

     (k)  "Subsidiary" means (1) any corporation or other entity of which
          securities or other ownership interests having ordinary voting power
          to elect a majority of the board of directors or other persons
          performing similar functions are at the time directly or indirectly
          owned by the Company, or (2) a partnership or limited liability
          company in which the Company or a Subsidiary of the Company is, at the

                                      -13-
<PAGE>

          date of determination, a general or limited partner of such
          partnership or a member of such limited liability company, but only if
          the Company or its Subsidiary is entitled to receive more than fifty
          percent of the assets of such partnership or limited liability company
          upon its dissolution.

     (l)  "Trading Day" means, as applied to any class of stock, any day on
          which the New York Stock Exchange or, if shares of such stock are not
          listed or admitted to trading on the New York Stock Exchange, the
          principal national securities exchange on which the shares of such
          stock are listed or admitted for trading or, if the shares of such
          stock are not listed or admitted for trading on any national
          securities exchange, the NASDAQ or, if the shares of such stock are
          not included therein, any similar interdealer system then in general
          use in which the shares of such stock are included, is open for the
          trading of securities generally and with respect to which information
          regarding the sale of securities included therein, or with respect to
          which sales information is reported, is generally available.

                                      -14-
<PAGE>

          THIS WARRANT CERTIFICATE is executed and delivered by the Company on
the date set forth below in Oceanport, New Jersey.

Dated:  September 18, 2000                   TELLIUM, INC.

                                             By: ___________________________

                                             Name: _________________________

                                             Title: ________________________

                                             Attested to:
                                             -----------

                                             By: ___________________________

                                             Name: _________________________

                                             Title: ________________________

                                      -1-
<PAGE>

                                   Exhibit A
                                   ---------

                                  ASSIGNMENT

                (To be signed only upon assignment of Warrant)

  FOR VALUE RECEIVED, the undersigned hereby sells, assigns and transfer unto

                        ______________________________
                                    (Name)

                        ______________________________

                        ______________________________
                                   (Address)

                        ______________________________
                           (Social Security Number)

the Warrant in the name of the undersigned and hereby appoints the Secretary of
the Company as the undersigned's attorney-in-fact to transfer said Warrant on
the books of the Company, with full power of substitution in the premises.

Date: __________, 20___

Signature of Registered Holder: ________________________________________________

Note:  The above signature must correspond with the name as written upon the
face of this Warrant Certificate in every particular without alteration or
enlargement or any change whatever unless this Warrant has been assigned.

                                      -1-
<PAGE>

                                   Exhibit B
                                   ---------

                             ELECTION TO PURCHASE

Tellium, Inc.
2 Crescent Place
P.O. Box 901
Oceanport, NJ 07757-0901
Attn: Chief Financial Officer

     The undersigned hereby irrevocably elects to exercise the right of purchase
represented by the within Warrant for and to purchase thereunder, shares of the
stock provided for herein, and requests that certificates for such shares be
issued in the name of

                        ______________________________
                                    (Name)

                        ______________________________

                        ______________________________
                                   (Address)

                        ______________________________
                           (Social Security Number)

and, if said number of shares will not be all the shares purchasable thereunder,
that a new Warrant Certificate for the balance remaining of the shares
purchasable under the within Warrant Certificate be registered in the name of
the undersigned holder of this Warrant or his Assignee as below indicated and
delivered to the address stated below.  By placing an X in the following blank,
the undersigned hereby elects to exercise the purchase right with respect to
__________ shares of such Common Stock through Warrant Conversion, as set forth
in Section 3 of the within Warrant.

Date: __________, 20___

Name of holder of this Warrant Certificate or Assignee: ________________________

Address: _______________________________________________________________________

Signature: _____________________________________________________________________

Note: The above signature must correspond with the name as written upon the face
of this Warrant Certificate in every particular without alteration or
enlargement or any change whatever unless this Warrant has been assigned.

                                      -1-

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