<PAGE>
 
                                                                   EXHIBIT 10.34

NEITHER THESE SECURITIES NOR THE SECURITIES INTO WHICH THESE SECURITIES ARE
EXERCISABLE HAVE BEEN REGISTERED WITH THE SECURITIES AND EXCHANGE COMMISSION OR
THE SECURITIES COMMISSION OF ANY STATE IN RELIANCE UPON AN EXEMPTION FROM
REGISTRATION UNDER SECURITIES ACT OF 1933, AS AMENDED (THE "SECURITIES ACT"),
AND, ACCORDINGLY, MAY NOT BE OFFERED OR SOLD EXCEPT PURSUANT TO AN EFFECTIVE
REGISTRATION STATEMENT UNDER THE SECURITIES ACT OR PURSUANT TO AN AVAILABLE
EXEMPTION FROM THE REGISTRATION REQUIREMENTS THEREUNDER AND IN COMPLIANCE WITH
APPLICABLE STATE SECURITIES OR BLUE SKY LAWS.


                             PHOENIX NETWORK, INC.

                                    WARRANT
                                    -------

                              Dated April 4, 1997


          Phoenix Network, Inc., a Delaware corporation (the "Company"), hereby
certifies that, for value received, ________________, or his registered assigns
("Holder"), is entitled, subject to the terms set forth below, to purchase from
the Company up to a total of ___________ shares of Common Stock, $.001 par value
per share (the "Common Stock"), of the Company (each such share, a "Warrant
Share" and all such shares, the "Warrant Shares") at an exercise price equal to
$2.3375 per share (as adjusted from time to time as provided in Section 8, the
"Exercise Price"), at any time and from time to time from and after the date
hereof and through and including April 4, 2002 (the "Expiration Date"), and
subject to the following terms and conditions:

          1.    Registration of Warrant.  The Company shall register this
                -----------------------                                  
Warrant, upon records to be maintained by the Company for that purpose (the
"Warrant Register"), in the name of the record Holder hereof from time to time.
The Company may deem and treat the registered Holder of this Warrant as the
absolute owner hereof for the purpose of any exercise hereof or any distribution
to the Holder, and for all other purposes, and the Company shall not be affected
by notice to the contrary.
<PAGE>
 
          2.   Registration of Transfers and Exchanges.
               --------------------------------------- 
 
               (a) The Company shall register the transfer of any portion of
this Warrant in the Warrant Register, upon surrender of this Warrant, with the
Form of Assignment attached hereto duly completed and signed, to the Transfer
Agent or to the Company at the office specified in or pursuant to Section 3(b),
provided, however that the Holder shall not make any transfers to any transferee
pursuant to this Section for the right to acquire less than 5,000 Warrant
Shares. Upon any such registration or transfer, a new warrant to purchase Common
Stock, in substantially the form of this Warrant (any such new warrant, a "New
Warrant"), evidencing the portion of this Warrant so transferred shall be issued
to the transferee and a New Warrant evidencing the remaining portion of this
Warrant not so transferred, if any, shall be issued to the transferring Holder.
The acceptance of the New Warrant by the transferee thereof shall be deemed the
acceptance of such transferee of all of the rights and obligations of a holder
of a Warrant.

               (b) This Warrant is exchangeable, upon the surrender hereof by
the Holder to the office of the Company specified in or pursuant to Section 3(b)
for one or more New Warrants, evidencing in the aggregate the right to purchase
the number of Warrant Shares which may then be purchased hereunder. Any such New
Warrant will be dated the date of such exchange.

          3.   Duration and Exercise of Warrants.
               --------------------------------- 

               (a) This Warrant shall be exercisable by the registered Holder on
any business day before 5:30 P.M., New York time, at any time and from time to
time on or after the date hereof to and including the Expiration Date. At 5:30
P.M., New York time on the Expiration Date, the portion of this Warrant not
exercised prior thereto shall be and become void and of no value.

               (b) Subject to Sections 2(b), 5 and 9, upon surrender of this
Warrant, with the Form of Election to Purchase attached hereto duly completed
and signed, to the Company at its office at 1687 Cole Blvd., Golden, CO 80401,
Attention: Chief Executive Officer, or at such other address as the Company may
specify in writing to the then registered Holder, and upon payment of the
Exercise Price multiplied by the number of Warrant Shares that the Holder
intends to purchase hereunder, in lawful money of the United States of America,
in cash or by certified or official bank check or checks, all as specified by
the Holder in the Form of Election to Purchase, the Company shall promptly (but
in no event later than 3 business days after the date of exercise) issue or
cause to be issued and cause to be delivered to or upon the written order of the
Holder and in such name or names as the Holder may designate, a certificate for
the Warrant Shares issuable upon such exercise, free of restrictive legends
other than as required by applicable law. Any person so designated by the Holder
to receive Warrant Shares shall be deemed to have become holder of record of
such Warrant Shares as of the Date of Exercise of this Warrant.

                                      -2-
<PAGE>
 
          A "Date of Exercise" means the date on which the Company shall have
received (i) this Warrant (or any New Warrant, as applicable), with the Form of
Election to Purchase attached hereto (or attached to such New Warrant)
appropriately completed and duly signed, and (ii) payment of the Exercise Price
for the number of Warrant Shares so indicated by the holder hereof to be
purchased.

          (c) This Warrant shall be exercisable, either in its entirety or, from
time to time, for a portion of the number of Warrant Shares.  If less than all
of the Warrant Shares which may be purchased under this Warrant are exercised at
any time, the Company shall issue or cause to be issued, at its expense, a New
Warrant evidencing the right to purchase the remaining number of Warrant Shares
for which no exercise has been evidenced by this Warrant.

     4.   Piggyback Registration Rights.  During the term of this Warrant
          -----------------------------                                  
the Company may not file any registration statement with the Securities and
Exchange Commission (other than registration statements of the Company filed on
Form S-8 or Form S-4 or, with respect to the Company's Series F and Series G
Convertible Preferred Stock only, on Form S-3, (provided, however, that such
exception with respect to such S-3 registration statements shall only be
available for the initially filed registration statements on such form
(including supplements thereto), but not additionally filed registration
statements in respect of such securities), each as promulgated under the
Securities Act of 1933, as amended, pursuant to which the Company is registering
securities pursuant to a Company employee benefit plan or pursuant to a merger,
acquisition or similar transaction) unless the Company provides the Holder with
not less than five 15 business days notice to each of the Holder and Robinson
Silverman Peace Aronsohn & Berman LLP, attention Eric Cohen, notice of its
intention to file such registration statement and provides the Purchaser the
option to include any or all of the applicable Warrant Shares therein.  The
piggyback registration rights granted to the Holder pursuant to this Section
shall continue until all of the Holder's Warrant Shares have been sold in
accordance with an effective registration statement or upon the expiration of
this Warrant.  The Company will pay all registration expenses in connection
therewith.

     5.   Payment of Taxes.  The Company will pay all documentary stamp
          ----------------                                             
taxes attributable to the issuance of Warrant Shares upon the exercise of this
Warrant; provided, however, that the Company shall not be required to pay any
tax which may be payable in respect of any transfer involved in the registration
of any certificates for Warrant Shares or Warrants in a name other than that of
the Holder, and the Company shall not be required to issue or cause to be issued
or deliver or cause to be delivered the certificates for Warrant Shares unless
or until the person or persons requesting the issuance thereof shall have paid
to the Company the amount of such tax or shall have established to the
satisfaction of the Company that such tax has been paid.  The Holder shall be
responsible for all other tax liability that may arise as a result of holding or
transferring this Warrant or receiving Warrant Shares upon exercise hereof.

                                      -3-
<PAGE>
 
          6.   Replacement of Warrant.  If this Warrant is mutilated, lost,
               ----------------------                                      
stolen or destroyed, the Company may in its discretion issue or cause to be
issued in exchange and substitution for and upon cancellation hereof, or in lieu
of and substitution for this Warrant, a New Warrant, but only upon receipt of
evidence reasonably satisfactory to the Company of such loss, theft or
destruction and indemnity, if requested, satisfactory to it.  Applicants for a
New Warrant under such circumstances shall also comply with such other
reasonable regulations and procedures and pay such other reasonable charges as
the Company may prescribe.


          7.   Reservation of Warrant Shares.  The Company covenants that it
               -----------------------------                                
will at all times reserve and keep available out of the aggregate of its
authorized but unissued Common Stock, solely for the purpose of enabling it to
issue Warrant Shares upon exercise of this Warrant as herein provided, the
number of Warrant Shares which are then issuable and deliverable upon the
exercise of this entire Warrant, free from preemptive rights or any other actual
contingent purchase rights of persons other than the Holders (taking into
account the adjustments and restrictions of Section 8).  The Company covenants
that all Warrant Shares that shall be so issuable and deliverable shall, upon
issuance and the payment of the applicable Exercise Price in accordance with the
terms hereof, be duly and validly authorized, issued and fully paid and
nonassessable.

          8.   Certain Adjustments.  The Exercise Price and number of Warrant
               -------------------                                           
Shares issuable upon exercise of this Warrant are subject to adjustment from
time to time as set forth in this Section 8.  Upon each such adjustment of the
Exercise Price pursuant to this Section 8, the Holder shall thereafter prior to
the Expiration Date be entitled to purchase, at the Exercise Price resulting
from such adjustment, the number of Warrant Shares obtained by multiplying the
Exercise Price in effect immediately prior to such adjustment by the number of
Warrant Shares issuable upon exercise of this Warrant immediately prior to such
adjustment and dividing the product thereof by the Exercise Price resulting from
such adjustment.

               (a) If the Company, at any time while this Warrant is
outstanding, (i) shall pay a stock dividend (except scheduled dividends paid on
outstanding preferred stock as of the date hereof which contain a stated divided
rate, and on the Company's Series G Preferred Convertible Stock of the Company)
or otherwise make a distribution or distributions on shares of its Common Stock
(as defined below) or on any other class of capital stock and not the Common
Stock) payable in shares of Common Stock, (ii) subdivide outstanding shares of
Common Stock into a larger number of shares, or (iii) combine outstanding shares
of Common Stock into a smaller number of shares, the Exercise Price shall be
multiplied by a fraction of which the numerator shall be the number of shares of
Common Stock (excluding treasury shares, if any) outstanding before such event
and of which the denominator shall be the number of shares of Common Stock
(excluding treasury shares, if any) outstanding after such event. Any adjustment
made pursuant to this Section shall become effective immediately after the
record date for the determination of stockholders entitled to receive such
dividend or distribution and shall become effective

                                      -4-
<PAGE>
 
immediately after the effective date in the case of a subdivision or
combination, and shall apply to successive subdivisions and combinations.

          (b) In case of any reclassification of the Common Stock, any
consolidation or merger of the Company with or into another person, the sale or
transfer of all or substantially all of the assets of the Company or any
compulsory share exchange pursuant to which the Common Stock is converted into
other securities, cash or property, then the Holder shall have the right
thereafter to exercise this Warrant only into the shares of stock and other
securities and property receivable upon or deemed to be held by holders of
Common Stock following such reclassification, consolidation, merger, sale,
transfer or share exchange, and the Holder shall be entitled upon such event to
receive such amount of securities or property equal to the amount of Warrant
Shares such Holder would have been entitled to had such Holder exercised this
Warrant immediately prior to such reclassification, consolidation, merger, sale,
transfer or share exchange.  The terms of any such consolidation, merger, sale,
transfer or share exchange shall include such terms so as to continue to give to
the Holder the right to receive the securities or property set forth in this
Section 8(b) upon any exercise following any such reclassification,
consolidation, merger, sale, transfer or share exchange.

          (c) If the Company, at any time while this Warrant is outstanding,
shall distribute to all holders of Common Stock (and not to holders of this
Warrant) evidences of its indebtedness or assets or rights or warrants to
subscribe for or purchase any security (excluding those referred to in Sections
8(a), (b) and (d)), then in each such case the Exercise Price shall be
determined by multiplying the Exercise Price in effect immediately prior to the
record date fixed for determination of stockholders entitled to receive such
distribution by a fraction of which the denominator shall be the Exercise Price
determined as of the record date mentioned above, and of which the numerator
shall be such Exercise Price on such record date less the then fair market value
at such record date of the portion of such assets or evidence of indebtedness so
distributed applicable to one outstanding share of Common Stock as determined by
the Company's independent certified public accountants that regularly examines
the financial statements of the Company (an "Appraiser").
                                             ---------   

          (d) If, at any time while this Warrant is outstanding, the Company
shall issue or cause to be issued rights or warrants to acquire or otherwise
sell or distribute shares of Common Stock to all holders of Common Stock for a
consideration per share less than the Exercise Price then in effect, then,
forthwith upon such issue or sale, the Exercise Price shall be reduced to the
price (calculated to the nearest cent) determined by dividing (i) an amount
equal to the sum of (A) the number of shares of Common Stock outstanding
immediately prior to such issue or sale multiplied by the Exercise Price, and
(B) the consideration, if any, received or receivable by the Company upon such
issue or sale by (ii) the total number of shares of Common Stock outstanding
immediately after such issue or sale.

          (e) For the purposes of this Section 8, the following clauses shall
also be applicable:

                                      -5-
<PAGE>
 
          (i)  Record Date.  In case the Company shall take a record of the
               -----------                                                 
holders of its Common Stock for the purpose of entitling them (A) to receive a
dividend or other distribution payable in Common Stock or in Convertible
Securities, or (B) to subscribe for or purchase Common Stock or Convertible
Securities, then such record date shall be deemed to be the date of the issue or
sale of the shares of Common Stock deemed to have been issued or sold upon the
declaration of such dividend or the making of such other distribution or the
date of the granting of such right of subscription or purchase, as the case may
be.

          (ii)  Treasury Shares.  The number of shares of Common Stock
                ---------------                                       
outstanding at any given time shall not include shares owned or held by or for
the account of the Company, and the disposition of any such shares shall be
considered an issue or sale of Common Stock.

     (f)  All calculations under this Section 8 shall be made to the nearest
cent or the nearest 1/100th of a share, as the case may be.

     (g)  Whenever the Exercise Price is adjusted pursuant to Section 8(c)
above, the Holder, after receipt of the determination by the Appraiser, shall
have the right to select an additional appraiser (which shall be a nationally
recognized accounting firm), in which case the adjustment shall be equal to the
average of the adjustments recommended by each of the Appraiser and such
appraiser. The Holder shall promptly mail or cause to be mailed to the Company,
a notice setting forth the Exercise Price after such adjustment and setting
forth a brief statement of the facts requiring such adjustment. Such adjustment
shall become effective immediately after the record date mentioned above.

     (h)  If:
                (i)      the Company shall declare a dividend (or any other
                         distribution) on its Common Stock; or

                (ii)     the Company shall declare a special nonrecurring cash
                         dividend on or a redemption of its Common Stock; or

                (iii)    the Company shall authorize the granting to all holders
                         of the Common Stock rights or warrants to subscribe for
                         or purchase any shares of capital stock of any class or
                         of any rights; or

                (iv)     the approval of any stockholders of the Company shall
                         be required in connection with any reclassification of
                         the Common Stock of the Company, any consolidation or

                                      -6-
<PAGE>
 
                         merger to which the Company is a party, any sale or
                         transfer of all or substantially all of the assets of
                         the Company, or any compulsory share exchange whereby
                         the Common Stock is converted into other securities,
                         cash or property; or

                (v)      the Company shall authorize the voluntary dissolution,
                         liquidation or winding up of the affairs of the
                         Company,

then the Company shall cause to be mailed to each Holder at their last addresses
as they shall appear upon the Warrant Register, at least 30 calendar days prior
to the applicable record or effective date hereinafter specified, a notice
stating (x) the date on which a record is to be taken for the purpose of such
dividend, distribution, redemption, rights or warrants, or if a record is not to
be taken, the date as of which the holders of Common Stock of record to be
entitled to such dividend, distributions, redemption, rights or warrants are to
be determined or (y) the date on which such reclassification, consolidation,
merger, sale, transfer or share exchange is expected to become effective or
close, and the date as of which it is expected that holders of Common Stock of
record shall be entitled to exchange their shares of Common Stock for
securities, cash or other property deliverable upon such reclassification,
consolidation, merger, sale, transfer, share exchange, dissolution, liquidation
or winding up; provided, however, that the failure to mail such notice or any
               --------  -------                                             
defect therein or in the mailing thereof shall not affect the validity of the
corporate action required to be specified in such notice.

     9.   Fractional Shares.  The Company shall not be required to issue or
          -----------------                                                
cause to be issued fractional Warrant Shares on the exercise of this Warrant.
The number of full Warrant Shares which shall be issuable upon the exercise of
this Warrant shall be computed on the basis of the aggregate number of Warrant
Shares purchasable on exercise of this Warrant so presented.  If any fraction of
a Warrant Share would, except for the provisions of this Section 9, be issuable
on the exercise of this Warrant, the Company shall pay an amount in cash equal
to the Exercise Price multiplied by such fraction.

     10.  Notices.  Any and all notices or other communications or
          -------                                                 
deliveries hereunder shall be in writing and shall be deemed given and effective
on the earliest of (i) the date of transmission, if such notice or communication
is delivered via facsimile at the facsimile telephone number specified in this
Section prior to 4:30 p.m. (Eastern Standard Time) on a business day, (ii) the
business day after the date of transmission, if such notice or communication is
delivered via facsimile at the facsimile telephone number specified in this
Section later than 4:30 p.m. (Eastern Standard Time) on any date and earlier
than 11:59 p.m. (Eastern Standard Time) on such date, (iii) the business day
following the date of mailing, if sent by nationally recognized overnight
courier service, or (iv) upon actual receipt by the party to whom such notice is
required to be given.  The addresses for such communications shall be:  (1) if
to the Company, to Phoenix 

                                      -7-
<PAGE>
 
Network, Inc., 1687 Cole Blvd., Golden, CO 80401, Attention: Chief Executive
Officer, or to facsimile no. (303) 205-3511, or (ii) if to the Holder, to the
Holder at the address or facsimile number appearing on the Warrant Register or
such other address or facsimile number as the Holder may provide to the Company
in accordance with this Section 10.

     11.  Warrant Agent.
          ------------- 

          (a) The Company shall serve as warrant agent under this Warrant.  Upon
thirty (30) days' notice to the Holder, the Company may appoint a new warrant
agent.

          (b) Any corporation into which the Company or any new warrant agent
may be merged or any corporation resulting from any consolidation to which the
Company or any new warrant agent shall be a party or any corporation to which
the Company or any new warrant agent transfers substantially all of its
corporate trust or shareholders services business shall be a successor warrant
agent under this Warrant without any further act.  Any such successor warrant
agent shall promptly cause notice of its succession as warrant agent to be
mailed (by first class mail, postage prepaid) to the Holder at the Holder's last
address as shown on the Warrant Register.

     12.  Miscellaneous.
          ------------- 

          (a) This Warrant shall be binding on and inure to the benefit of the
parties hereto and their respective successors and permitted assigns.  This
Warrant may be amended only in writing signed by the Company and the Holder.

          (b) Subject to Section 12(a), above, nothing in this Warrant shall be
construed to give to any person or corporation other than the Company and the
Holder any legal or equitable right, remedy or cause under this Warrant; this
Warrant shall be for the sole and exclusive benefit of the Company and the
Holder.

          (c) This Warrant shall be governed by and construed and enforced in
accordance with the internal laws of the State of New York without regard to the
principles of conflicts of law thereof.

          (d) The headings herein are for convenience only, do not constitute a
part of this Warrant and shall not be deemed to limit or affect any of the
provisions hereof.

          (e) In case any one or more of the provisions of this Warrant shall be
invalid or unenforceable in any respect, the validity and enforceability of the
remaining terms and provisions of this Warrant shall not in any way be affected
or impaired thereby and the parties will attempt in good faith to agree upon a
valid and enforceable provision which shall be a commercially reasonable
substitute therefor, and upon so agreeing, shall incorporate such substitute
provision in this Warrant.

                                      -8-
<PAGE>
 
          IN WITNESS WHEREOF, the Company has caused this Warrant to be duly
executed by its authorized officer as of the date first indicated above.


                              PHOENIX NETWORK, INC.



                              By:______________________________

                              Name:____________________________

                              Title:___________________________


<PAGE>
 
                         FORM OF ELECTION TO PURCHASE

(To be executed by the Holder to exercise the right to purchase shares of Common
Stock under the foregoing Warrant)

To Phoenix Network, Inc.:

          In accordance with the Warrant enclosed with this Form of Election to
Purchase, the undersigned hereby irrevocably elects to purchase  _____________
shares of Common Stock ("Common Stock"), $.001 par value per share, of Phoenix
Network, Inc. and encloses herewith $________ in cash, certified or official
bank check or checks, which sum represents the aggregate Exercise Price (as
defined in the Warrant) for the number of shares of Common Stock to which this
Form of Election to Purchase relates, together with any applicable taxes payable
by the undersigned pursuant to the Warrant.

          The undersigned requests that certificates for the shares of Common
Stock issuable upon this exercise be issued in the name of

                                                PLEASE INSERT SOCIAL SECURITY OR
                                                TAX IDENTIFICATION NUMBER
                                                
                                                ________________________________

________________________________________________________________________________
                        (Please print name and address)

________________________________________________________________________________

________________________________________________________________________________

          If the number of shares of Common Stock issuable upon this exercise
shall not be all of the shares of Common Stock which the undersigned is entitled
to purchase in accordance with the enclosed Warrant, the undersigned requests
that a New Warrant (as defined in the Warrant) evidencing the right to purchase
the shares of Common Stock not issuable pursuant to the exercise evidenced
hereby be issued in the name of and delivered to:

________________________________________________________________________________
                        (Please print name and address)

________________________________________________________________________________

________________________________________________________________________________

Dated:  _____,______                            Name of Holder:

                                                (Print)_________________________

                                                (By:)___________________________
                                                (Name:)
                                                (Title:)
                                                (Signature must conform in all
                                                respects to name of holder as
                                                specified on the face of the
                                                Warrant)

                      
<PAGE>
 
           [To be completed and signed only upon transfer of Warrant]

          FOR VALUE RECEIVED, the undersigned hereby sells, assigns and
transfers unto ________________________________ the right represented by the
within Warrant to purchase  ____________ shares of Common Stock of Phoenix
Network, Inc. to which the within Warrant relates and appoints ________________
attorney to transfer said right on the books of Phoenix Network, Inc. with full
power of substitution in the premises.

Dated:

_______________, ____


                              __________________________________________________
                              (Signature must conform in all respects to name of
                              holder as specified on the face of the Warrant)


                              __________________________________________________
                              Address of Transferee

                              __________________________________________________

                              __________________________________________________



In the presence of:


________________________