Document:

<PAGE>

                                                                     Exhibit 4.4

                         FIRST SUPPLEMENT TO INDENTURE

     This First Supplement to Indenture (this "Supplement") is dated as of
December 19, 2000 by and among Carrols Corporation, a Delaware corporation (the
"Company"), Taco Cabana, Inc., a Delaware corporation, TP Acquisition Corp., a
Texas corporation, T.C. Management, Inc., a Delaware corporation, Get Real,
Inc., a Delaware corporation, Taco Cabana Management, Inc., a Texas corporation,
Texas Taco Cabana, L.P., a Texas limited partnership, TC Lease Holdings III, (V)
and (VI), Inc., a Texas corporation, Cabana Bevco, LLC, a Texas limited
liability company, TC Bevco Management, LLC, a Texas limited liability company,
TC Bevco Holding, LLC, a Texas limited liability company, TC Bevco, LLC, a Texas
limited liability company, Cabana Beverages, Inc., a Texas corporation, Two
Pesos Liquor Corp., a Texas corporation, and Rosa Beverages, Inc., a Texas
corporation (collectively, the "Additional Guarantors"), and The Bank of New
York, a New York banking corporation (the "Successor Trustee"), as successor
Trustee to IBJ Schroder Bank & Trust Company (the "Original Trustee") with
respect to the Company's Series A 9 1/2% Senior Subordinated Notes due 2008 and
Series B 9 1/2% Senior Subordinated Notes due 2008 (the "Notes").  Capitalized
terms used but not otherwise defined in this Supplement shall have the meanings
ascribed to such terms in the Indenture as amended and supplemented from time to
time in accordance with its terms.

     WHEREAS, the Company, the Guarantors named therein and the Original Trustee
entered into the Indenture, dated as of November 24, 1998 (the "Indenture"); and

     WHEREAS, pursuant to Section 4.11 of the Indenture, Restricted Subsidiaries
of the Company meeting certain qualifications described therein are required to
execute and deliver to the Trustee a supplemental indenture that shall
unconditionally guarantee all of the Company's obligations under the Notes and
Indenture.

     NOW, THEREFORE, in consideration of the premises and for other good and
valuable consideration, the receipt and sufficiency of which are hereby
acknowledged, the parties hereby agree, for the equal and proportionate benefit
of all Holders of the Notes, as follows:

                                   ARTICLE I
                              SUBSIDIARY GUARANTY

     Section 1.01  Guaranty.  Each of the Additional Guarantors hereby
                   --------
unconditionally guarantees all of the Company's obligations under the Notes and
the Indenture on the terms set forth in Article Eleven of the Indenture.

                                  ARTICLE II
                           MISCELLANEOUS PROVISIONS

     Section 2.01  Instruments to be Read Together.  This Supplement is an
                   -------------------------------
indenture supplement to and in implementation of the Indenture, and said
Indenture and this Supplement shall henceforth be read together.
<PAGE>

     Section 2.02  Confirmation.  The Indenture, as amended and supplemented by
                   ------------
this Supplement, is in all respects confirmed and preserved.

     Section 2.03  Counterparts.  This Supplement may be executed in any number
                   ------------
of counterparts, each of which, when so executed, shall be deemed to be an
original, but all of which shall together constitute one and the same
instrument.

     Section 2.04  Effectiveness.  This Supplement shall become effective
                   -------------
immediately upon its execution in accordance with the provisions of the
Indenture.

     Section 2.05  GOVERNING LAW.  THIS SUPPLEMENT SHALL BE GOVERNED BY AND
                   -------------
CONSTRUED IN ACCORDANCE WITH THE LAWS OF THE STATE OF NEW YORK, AS APPLIED TO
CONTRACTS MADE AND PERFORMED WITHIN THE STATE OF NEW YORK, WITHOUT REGARD TO THE
CONFLICTS OF LAWS RULES THEREOF.

     Section 2.06  Disclaimer of Trustee's Responsibility.  In executing this
                   --------------------------------------
Supplement, the Successor Trustee shall be entitled to all the privileges and
immunities afforded to the Trustee under the terms and conditions of the
Indenture.

                                       2
<PAGE>

          IN WITNESS WHEREOF, the parties hereto have caused this Supplement to
Indenture to be duly executed as of the date first above written.

                              CARROLS CORPORATION

                              By:  /s/ Joseph Zirkman
                                   ------------------------------------
                              Name:  Joseph Zirkman
                              Its:  Vice President

                              TACO CABANA, INC.

                              By:  /s/ Joseph Zirkman
                                   ------------------------------------
                              Name:  Joseph Zirkman
                              Its:  Vice President

                              TP ACQUISITION CORP.

                              By:  /s/ Joseph Zirkman
                                   ------------------------------------
                              Name:  Joseph Zirkman
                              Its:  Vice President

                              T.C. MANAGEMENT, INC.

                              By:  /s/ Joseph Zirkman
                                   ------------------------------------
                              Name:  Joseph Zirkman
                              Its:  Vice President

                                       3
<PAGE>

                              GET REAL, INC.

                              By:  /s/ Clayton E. Wilhite
                                   ------------------------------------
                              Name:  Clayton E. Wilhite
                              Its:  Vice President

                              TACO CABANA MANAGEMENT, INC.

                              By:  /s/ Joseph Zirkman
                                   ------------------------------------
                              Name:  Joseph Zirkman
                              Its:  Vice President

                              TEXAS TACO CABANA, L.P.

                              By:  TACO CABANA MANAGEMENT, INC.,
                                   its General Partner

                              By:  /s/ Joseph Zirkman
                                   ------------------------------------
                              Name:  Joseph Zirkman
                              Its:  Vice President

                              TC LEASE HOLDINGS III, (V) AND (VI), INC.

                              By: /s/ Becky Rainey
                                  -------------------------------------
                              Name:  Becky Rainey
                              Its:  Vice President and General Counsel

                              CABANA BEVCO, LLC

                              By: /s/ James Jenkins
                                  -------------------------------------
                              Name:  James Jenkins
                              Its:  Manager

                                       4
<PAGE>

                              TC BEVCO MANAGEMENT, LLC

                              By: /s/ James Jenkins
                                  -----------------------------------
                              Name:  James Jenkins
                              Its:  Manager

                              TC BEVCO HOLDING, LLC

                              By: /s/ James Jenkins
                                  -----------------------------------
                              Name:  James Jenkins
                              Its:  Manager

                              TC BEVCO, LLC

                              By: /s/ James Jenkins
                                  -----------------------------------
                              Name:  James Jenkins
                              Its:  Manager

                              CABANA BEVERAGES, INC.

                              By: /s/ James Jenkins
                                  -----------------------------------
                              Name:  James Jenkins
                              Its:  President

                              TWO PESOS LIQUOR CORP.

                              By: /s/ James Jenkins
                                  -----------------------------------
                              Name:  James Jenkins
                              Its:  President

                              ROSA BEVERAGES, INC.

                              By: /s/ James Jenkins
                                  -----------------------------------
                              Name:  James Jenkins
                              Its:  President

                                       5
<PAGE>

                              THE BANK OF NEW YORK

                              By: /s/ Michael C. Daly
                                  -----------------------------------
                              Name:  Michael C. Daly
                              Its:  Assistant Vice President

                                       6<PAGE>

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.

                                                                   EXHIBIT 10.29

                                                                  Execution Copy

                              WARRANT CERTIFICATE

                                 TELLIUM, INC.

                                "C" WARRANTS TO
                             Purchase Common Stock

Certificate                                                     Certificate for
No. 1                                                      750,000 "C" Warrants

     THIS WARRANT CERTIFICATE CERTIFIES THAT QWEST INVESTMENT COMPANY, a
Delaware corporation ("QIC"), or its registered assigns, is the registered
holder of the number of "C" Warrants (the "Warrants") set forth above which were
granted by Tellium, Inc., a Delaware corporation (the "Company") to QIC for
$1.00 and other good and valuable consideration.  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 $7.00 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 2 HEREOF, 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.
<PAGE>

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.

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

     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  No Transfer.  The Warrants and shares of Common Stock to be issued
          -----------
          pursuant to the exercise of the Warrant (the "Warrant Shares") shall
          not be sold, transferred, assigned, pledged, encumbered or otherwise
          disposed of (each, a "Transfer") except upon the conditions specified
          in this Section 2.

     2.3  Legend.   The Warrant Shares shall (unless otherwise permitted by the
          ------
          provisions of Sections 2.4 and 2.5) be stamped or otherwise imprinted
          with a legend in substantially the following form:

          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 2 OF THE WARRANT CERTIFICATE, 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

                                      -2-
<PAGE>

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.

          SECURITIES REPRESENTED HEREBY REGISTERED IN THE NAME OF THE HOLDER
          HEREOF.

     2.4  Notice.  (a)  Subject to Sections 2.4(b) and 2.4(c), QIC agrees, prior
          ------
          to any Transfer of Warrants (or Warrant Shares), to give written
          notice to comply with the provisions of this Section 2.  Each such
          notice shall be accompanied by the written opinion (addressed to the
          Company by counsel for the holder of such Warrant or Warrant Shares
          and stating that in the opinion of such counsel (which opinion and
          counsel shall be reasonably satisfactory to the Company) such proposed
          Transfer does not involve a transaction requiring registration of such
          Warrant or Warrant Shares under the Securities Act) and, except in
          respect of sales pursuant to Securities Act Rule 144 or a registration
          statement effective pursuant to the Securities Act of 1933, as
          amended, the transferee's agreement in writing to be subject to the
          terms of this Section 2 to the same extent as if such transferee were
          originally a signatory to this Agreement.  QIC shall thereupon be
          entitled to Transfer such shares.  Each certificate or other
          instrument evidencing the Warrant or Warrant Shares issued upon the
          Transfer of any such Warrant or Warrant Shares (and each certificate
          or other instrument evidencing any untransferred balance of such
          Warrant or Warrant Shares) shall bear the legend set forth in Section
          2.3 unless (x) in such opinion of counsel registration of any future
          Transfer is not required by the applicable provisions of the
          Securities Act or (y) the Company shall have waived the requirement of
          such legends; provided, however, that such legend shall not be
          required on any certificate or other instrument evidencing the
          securities issued upon such Transfer in the event such Transfer shall
          be made in compliance with the requirements of Securities Act Rule 144
          and the transferee is not an affiliate (as defined in Rule 144 of the
          Securities Act) of the Company.

          (b)  Unless and until the "C" Warrants are fully exercisable in
               accordance with the terms set forth in the applicable Warrant
               Certificate, and except for a Transfer to an Affiliate (as
               defined in Section 21) of QIC, the "C" Warrants (and Warrant
               Shares) shall not be Transferred without the prior written
               consent of the Company, which shall not be unreasonably withheld
               (it being understood and agreed that a Transfer to a party that
               QIC could reasonably determine is a competitor of the Company or
               to a party that, after reasonable inquiry, QIC knows or has
               reason to know is asserting a material claim against (or an
               adverse party to a litigation or arbitration with) the Company
               are examples of circumstances where the Company may withhold its
               consent under this Section 2.4(b)).

     2.5  Termination.  Notwithstanding the foregoing provisions of this Section
          -----------
          2, the restrictions imposed by this Section 2 upon the transferability
          of the Warrant Shares shall cease and terminate when (i) any such
          shares are sold or otherwise disposed of pursuant to an effective
          registration statement under the Securities Act

                                      -3-
<PAGE>

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.

          or as otherwise contemplated by Section 2.4 and, pursuant to Section
          2.4, the securities so transferred are not required to bear the legend
          set forth in Section 2.3 or (ii) the holder of such shares has met the
          requirements for Transfer of such shares pursuant to paragraph (k) of
          Securities Rule 144. Whenever the restrictions imposed by this Section
          2 shall terminate as to any Warrant Shares, as herein provided, QIC
          shall be entitled to receive from the Company, without expense, a new
          certificate representing such Warrant Shares not bearing the
          restrictive legend set forth in Section 2.3 and not containing any
          other reference to the restrictions imposed by this Section 2.

     2.6  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 exercisable in whole or in part in accordance with the
          following:

          (a)  If Qwest has paid (***) pursuant to the Procurement Agreement
               dated as of September 18, 2000 between the Company and Qwest, as
               amended by the First Amendment to the Procurement Agreement dated
               as of the date hereof (the "Procurement Agreement"), (***)
               Warrants shall be 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

                                      -4-
<PAGE>

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.

               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 if they have not become exercisable prior to the
               sixth (6th) anniversary of the date hereof upon such sixth (6th)
               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 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

                                      -5-
<PAGE>

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 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
               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 the 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

                                      -6-
<PAGE>

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.

               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
          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 $7.00 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

                                      -7-
<PAGE>

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.

          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 "Excluded Stock," as defined in
          Article IV of the Company's Amended and Restated Certificate of
          Incorporation as of the date hereof), 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 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

                                      -8-
<PAGE>

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.

          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 Certificate.
          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.   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.   Covenants and Representations.
     -----------------------------

     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

                                      -9-
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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.

          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.

     8.5  Corporate Authorization.  The execution, delivery and performance by
          -----------------------
          the Company of its obligations under this Warrant Certificate and the
          Stockholder's Agreement (the "Core Agreements"), and the consummation
          by the Company of the transactions contemplated thereby, and the
          issuance by the Company of these Warrants and the Warrant Shares are
          within the corporate power and authority of the Company, and, have
          been duly authorized by all necessary corporate action.  The Core
          Agreements have been duly and validly authorized, executed and
          delivered by the Company and, subject to their execution by the other
          parties thereto, constitute a valid and binding obligation of the
          Company, enforceable against the Company in accordance with their
          terms, subject to bankruptcy, insolvency, reorganization, moratorium
          and similar laws of general applicability affecting creditors' rights
          and to general equity principles.

     8.6  Consents and Approvals.  The execution, delivery and performance by
          ----------------------
          the Company of its obligations under the Core Agreements and the
          consummation by the Company of the transactions contemplated thereby,
          and the issuance by the Company of these Warrants and the Warrant
          Shares do not and will not require any consent, approval or action by
          or in respect of, or any declaration, filing or registration with, and
          Governmental Authority or other third party, other than

                                      -10-
<PAGE>

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.

          compliance with the applicable requirements of the Securities Act of
          1933, as amended (the "Securities Act") and any applicable state
          securities and "blue sky" laws in connection with the offering, sale
          and delivery of the Warrant Shares.

     8.7  Non-Contravention.  The execution, delivery and performance by the
          -----------------
          Company of the Core Agreements and the consummation by the Company of
          the transactions contemplated thereby, and the issuance by the Company
          of these Warrants and the Warrant Shares do not and will not, with or
          without the giving of notice, the lapse of time or both (i) contravene
          or conflict with the Amended and Restated Certificate of Incorporation
          or Bylaws of the Company, (ii) contravene or conflict with or
          constitute a violation of any provision of any law, rule, regulation,
          judgment, injunction, order or decree binding upon or applicable to
          the Company, (iii) contravene or conflict with or constitute a
          violation of or a default under, or give rise to any right of
          termination, cancellation or acceleration of any right or obligation
          of the Company or to a loss of any benefit to which the Company is
          entitled, under any provision of (A) any material agreement, contract,
          indenture, lease or other instrument binding upon the Company or (B)
          any material license, franchise, permit or other similar authorization
          held by the Company, or (iv) result in the creation or imposition of
          any lien on any asset of the Company.

     8.8  Exempt Sale.  Assuming the accuracy of the representations and
          -----------
          warranties of QIC contained in Section 22 hereof, the offer, sale and
          issuance of the Warrants and Warrant Shares in accordance with this
          Warrant Certificate will be exempt from the registration requirements
          of the Securities Act, and will have been registered or qualified (or
          are exempt from registration and qualification) under the
          registration, permit or qualification requirements of all applicable
          state securities laws.

     8.9.  Corporate Organization.  The Company is a corporation duly organized,
           ----------------------
          validly existing and in good standing under the laws of the State of
          Delaware and has all requisite power and authority and all necessary
          governmental franchises, licenses, permits, authorizations and
          approvals to own or lease and operate its properties and assets and to
          carry on its business as it is now being conducted, and is duly
          qualified or licensed as a foreign corporation to do business and in
          good standing in each jurisdiction in which the conduct or nature of
          the business conducted by it or the character or location of the
          properties owned or leased by it makes such qualification or licensing
          necessary, except where the failure to be so qualified or licensed
          would not have a Material Adverse Effect.  The Company has provided
          QIC with a true and complete copy of its Amended and Restated
          Certificate of Incorporation as in effect on the date hereof.
          "Material Adverse Effect" shall mean, when used with respect to the
          Company, any change, effect or circumstance that, individually or when
          taken together with all other such changes, effects or circumstances,
          is or would reasonably be expected to be materially adverse to the

                                      -11-
<PAGE>

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.

          financial condition, business, properties, assets, prospects or
          operations taken as a whole of the Company.

     8.10.  Capitalization.
            --------------

          As of the date hereof, the authorized capital stock of the Company
          consists of the following:

               (a)  26,661,150 shares of Preferred Stock, of which (A)
                    10,322,917 shares are designated as Series A Preferred
                    Stock, 10,089,584 of which are issued and outstanding, and
                    233,333 of which are reserved for issuance upon conversion
                    of the Series B Preferred Stock, (B) 233,333 shares are
                    designated Series B Preferred Stock, 233,333 of which are
                    issued and outstanding, (C) 2,593,974 shares are designated
                    Series C Preferred Stock, of which 2,564,465 are outstanding
                    and 29,509 are reserved for issuance upon exercise of
                    warrants issued or issuable to Comdisco, Inc., (D) 6,010,926
                    shares are designated Series D Preferred Stock, of which
                    6,010,926 are issued and outstanding and (E) 7,500,000
                    shares are designated Series E Preferred Stock, of which
                    7,274,413 are issued and outstanding.  As of the date
                    hereof, there are 113,320,152 shares of Common Stock
                    issuable on conversion of the issued and outstanding shares
                    of Series A, B, C and D Preferred Stock.

               (b)  900,000,000 shares of Common Stock, 59,084,039 shares of
                    which are issued and outstanding.

          Section 8.10 of the Company Disclosure Schedule sets forth a summary
          of all outstanding stock options and warrants of the Company,
          indicating the number of shares and type of capital stock issuable
          upon exercise thereof.  As of the date hereof, 49,960,242 shares of
          Common Stock have been reserved for issuance upon exercise of such
          stock options and 14,629,644 shares of Common Stock have been reserved
          for issuance upon exercise of such warrants (or upon conversion of
          shares of Series C Preferred Stock issuable upon exercise of such
          warrants).  Except as disclosed in Section 8.10 of the Company
          Disclosure Schedule, there are no options, warrants, exchange rights,
          subscription rights or other agreements, commitments or rights to
          purchase or otherwise acquire from the Company, or agreements,
          commitments or obligations of the Company to issue or sell, any
          capital stock, voting securities or securities convertible into or
          exchangeable or exercisable for capital stock or voting securities of
          the Company, other than those contemplated by this Warrant
          Certificate.

     8.11.  Compliance With Laws; No Defaults.  The Company is not in violation
            ---------------------------------
          of or default under, and no condition exists that with notice or lapse
          of time or both

                                      -12-
<PAGE>

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.

          would constitute a violation of or default under, any applicable
          provisions of any law, statute, ordinance, regulation, judgment,
          order, injunction, permit, license, certificate or other
          authorization, or its governing instruments, except for any
          violations, defaults or conditions that have not had and could not
          reasonably be expected to have a Material Adverse Effect on the
          Company.

     8.12.  Taxes.  The Company has (i) timely filed all material Tax Returns
            -----
          required to be filed (taking into account any extension of time within
          which to file any Tax Return that has been granted by the relevant
          taxing authority) for all taxable periods ending on or prior to the
          date hereof, and such Tax Returns are true, complete and correct in
          all material respects, (ii) paid or accrued all material taxes shown
          to be due and payable on such Tax Returns, and (iii) properly accrued
          all material taxes for periods subsequent to the periods covered by
          such Tax Returns.  There are currently no actions, suits, proceedings,
          investigations, audits or claims now pending against it in respect of
          any taxes.  "Tax Return" shall mean any return, declaration, report,
          claim for refund or information return or statement relating to any
          schedule, supporting information or attachment thereto, and including
          any amendment thereof.

     8.13.  Financial Statements.
            --------------------

          (a)  The Company has delivered to Qwest the following financial
               statements (collectively, the "Company Financial Statements"):

               (i)  the consolidated audited balance sheet of the Company as of
                    December 31, 2000 (the "Balance Sheet") and December 31,
                    1999, and the related consolidated statements of operations,
                    consolidated statements of changes in stockholders' equity
                    and consolidated statements of cash flows for the year ended
                    December 31, 1998, December 31, 1999, and December 31, 2000,
                    together with the notes thereto, audited by, and accompanied
                    by the report thereon, of Ernst & Young LLP relating to 1998
                    and Deloitte & Touche relating to 1999 and 2000.

          (b)  Each of the Company Financial Statements has been prepared in
               accordance with United States generally accepted accounting
               principles applied on a consistent basis, are correct and
               complete in all material respects and fairly present in all
               material respects the financial position of the Company as of the
               respective dates thereto and the results of its operations and
               its cash flows for the respective periods then ended.  The
               accounting records underlying the Company Financial Statements
               accurately and fairly reflect, in reasonable detail, the
               transactions of the Company, reflect only valid transactions, and
               fairly present in all material respects the basis for the
               financial position, the results of operations, and

                                      -13-
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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.

               the changes in financial position set forth in the Company
               Financial Statements and the Company's books of account have been
               maintained on a consistent basis in accordance with acceptable
               business practice.

   8.14.  Subsidiaries.  Except as set forth in the Company Disclosure
          ------------
          Schedule, the Company does not hold or own, directly or indirectly,
          any capital stock or other equity securities of any other corporation,
          or have any direct or indirect equity or ownership interest in any
          association, partnership, joint venture or other entity.

   8.15.  Absence of Undisclosed Liabilities and Decrease in Assets.  The
          ---------------------------------------------------------
          Company does not have any Liabilities, except those Liabilities which
          are (a) fully reflected or in the aggregate adequately reserved
          against in the Balance Sheet (including any notes thereto), or (b)
          incurred in the ordinary course of business since December 31, 2000
          and consistent with past practices and in the aggregate are not
          material to the Company.  Since the date of the Balance Sheet, there
          has been no decrease in the total assets or current assets of the
          Company other than in the ordinary course of business consistent with
          past practice.  Liability shall mean any liability or obligation,
          including any direct or indirect indebtedness, claim, loss, damage,
          deficiency (including deferred income tax and other net tax
          deficiencies and interest and penalties with respect to taxes due and
          unpaid), cost, expense, obligation, guarantee or responsibility,
          whether accrued, absolute or contingent, fixed or unfixed, liquidated
          or unliquidated, secured or unsecured.

   8.16.  Litigation.  There is no claim, action, suit, investigation or
          ----------
          proceeding pending or threatened against or affecting, the Company or
          any of its properties or assets before any court or arbitrator or any
          Governmental Authority that, if adversely determined, would have a
          Material Adverse Effect on the Company.

   8.17.  Disclosure.  None of the representations and warranties of the
          ----------
          Company contained herein or in the Company Disclosure Schedule
          provided to QIC contains any untrue statement of a material fact or
          omits to state a material fact necessary to make the statements
          contained herein or therein not misleading in light of the
          circumstances in which it was made.

   8.18.  No Other Representations or Warranties.  Except for the
          --------------------------------------
          representations and warranties of the Company contained in this
          Section 8, the Company has not made, and QIC may not rely on, any
          representation or warranty with respect to the Company or the
          transactions contemplated by this Warrant Certificate.

   8.19.  No Demand Rights.  The Company has provided QIC with a true and
          ----------------
          complete copy of the Amended and Restated Stockholders Agreement dated
          as of September 19, 2000 by and among the Company and the other
          parties thereto as in effect on the date hereof.  Except as set forth
          in the Company Disclosure Schedule, the Company is presently not under
          any obligation and has not granted

                                      -14-
<PAGE>

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.

          any rights to demand registration of the Company's securities under
          the Securities Act.

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

                                      -15-
<PAGE>

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.

     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 Qwest
     Investment Company, 1801 California Street, Denver, CO  80202, 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

                                      -16-
<PAGE>

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.

     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 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

                                      -17-
<PAGE>

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.

     consolidation, or its parent if the parent issues securities to the
     Company's security 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)  "Affiliate" means with respect to any person or entity, any other
          person or entity directly or indirectly controlling, controlled by or
          under common control with such first person or entity (for purposes of
          this definition, "control" as used with respect to a person or entity,
          shall mean the possession, directly or indirectly, of the power to
          direct or cause the direction of management and policies of such
          person or entity, whether by ownership of voting securities, by
          contract or otherwise).

     (b)  "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.

     (c)  "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.

     (d)  "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.

                                      -18-
<PAGE>

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.

     (e)  "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.

     (f)  "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.

     (g)  "Expiration Time" means 5:00 p.m., New York time, on the later of (i)
          the sixth (6th) anniversary of the date hereof 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.

     (h)  "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.

     (i)  "Governmental Authority" shall mean any governmental or regulatory
          body, court, agency, official or authority.

                                      -19-
<PAGE>

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.

     (j)  "Qwest" means Qwest Communications Corporation.

     (k)  "Stockholder's Agreement" means the Supplemental Stockholders'
          Agreement, dated as of the date hereof, by and between the Company and
          QIC.

     (l)  "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.

     (m)  "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.

22.  Representations and Warranties of QIC.  QIC hereby represents and warrants
     -------------------------------------
     to the Company as of the date hereof as follows:

     22.1  Power and Authority.  QIC has full power and authority to enter into
           -------------------
          this Agreement, to perform its obligations hereunder and to consummate
          the transactions contemplated hereby.  All necessary corporate action
          has been taken by QIC with respect to the execution and delivery of
          this Agreement and the consummation of the transactions contemplated
          hereby.  This Agreement has been duly executed and delivered by, and,
          assuming the due authorization, execution and delivery thereof by the
          Company, constitutes a valid and binding obligation of QIC,
          enforceable against QIC in accordance with its terms, subject to
          bankruptcy, insolvency, reorganization, moratorium and similar laws of
          general applicability affecting creditors' rights and to general
          equity principles.

     22.2  Governmental Consent, Etc. In reliance on the representations of the
           --------------------------
          Company contained herein, no consent, approval or authorization of, or
          designation, declaration or filing with, any Governmental Authority on
          the part of QIC is

                                      -20-
<PAGE>

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.

          required in connection with the valid execution and delivery of this
          Agreement, or the offer, sale or issuance of the Warrants and Warrant
          Shares, or the consummation of any other transactions contemplated
          hereby, except such filings as may be required to be made with the
          Securities and Exchange Commission and the National Association of
          Securities Dealers, Inc.

     22.3  Investment Representations.  (a) QIC is and will be acquiring the
           --------------------------
          Warrants and the Warrant Shares to be issued upon exercise hereof, for
          its own account, for investment and not with a view to the
          distribution thereof within the meaning of the Securities Act except
          that QIC may make certain transfers which will not result in a
          violation of the Securities Act.

          (b)  QIC understands that (i) the Warrants (and the Warrant Shares to
               be issued upon exercise thereof) have not been registered under
               the Securities Act by reason of their issuance by the Company in
               transactions exempt from the registration requirements of the
               Securities Act and the Company's reliance on such exemption is
               predicated upon QIC's representations set forth herein and (ii)
               the Warrants (and the Warrant Shares to be issued upon exercise
               thereof) must be held by QIC indefinitely unless a subsequent
               disposition thereof is registered under the Securities Act or is
               exempt from registration.

          (c)  QIC further understands that, with respect to the Warrants (and
               the Warrant Shares to be issued upon exercise thereof), the
               exemption from registration afforded by Rule 144 (the provisions
               of which are known to QIC) promulgated under the Securities Act
               depends on the satisfaction of various conditions, and that, if
               applicable, Rule 144 may afford a basis for sales only in limited
               amounts.

          (d)  QIC is an "accredited investor" as such term is defined in Rule
               501 promulgated under the Securities Act, with its principal
               executive offices located at the address set forth in Section 12.

     22.4  Affiliate Status.  QIC is a wholly-owned subsidiary of Qwest Services
           ----------------
          Corporation, the parent company of Qwest Communications Corporation.

                                      -21-
<PAGE>

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.

     IN WITNESS WHEREOF, the parties have executed this Warrant Certificate on
the day set forth below in Oceanport, New Jersey.

                                    TELLIUM, INC.

                              By:      /s/ Nicholas DeVito
                                   ------------------------------
                                    Name:  Nicholas DeVito
                                    Title: V.P. Business Development

Dated April 10, 2001

                                    QWEST INVESTMENT COMPANY

                              By:      /s/
                                   ------------------------------
                                    Name:
                                    Title:

                                      -22-
<PAGE>

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.

                                   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: __________, 2001

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 the Warrant has been assigned.
<PAGE>

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.

                                   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 Certificate.

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 Certificate has been
assigned.

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