<PAGE>   1
                                                                     EXHIBIT 4.2



                           CERTIFICATE OF DESIGNATIONS
                                       OF

                 CUMULATIVE REDEEMABLE PREFERRED STOCK, SERIES C

                                       OF

                              BARGO ENERGY COMPANY

                         Pursuant to Article 2.13 of the
                         Texas Business Corporation Act

     Bargo Energy Company, a corporation organized and existing under the laws
of the State of Texas (the "Corporation"), DOES HEREBY CERTIFY that, pursuant to
the authority conferred on the Board of Directors of the Corporation by the
Articles of Incorporation of the Corporation and in accordance with Article 2.13
of the Texas Business Corporation Act, on March ___, 2000, the Board of
Directors of the Corporation duly adopted, by all necessary action on the part
of the Corporation, the following resolutions establishing and designating a
series of its Preferred Stock, par value $.01 per share, designated "Cumulative
Redeemable Preferred Stock, Series C" and fixing and determining the relative
rights and preferences thereof-

     RESOLVED, that pursuant to the authority vested in the Board of Directors
of the Corporation (the "Board of Directors") in accordance with the provisions
of its Articles of Incorporation, a series of Preferred Stock, par value $.01
per share, of the Corporation is hereby created, and that the designation and
number of shares thereof and the preferences, limitations and relative rights
thereof are as follows:

     Section 1. DESIGNATION, NUMBER OF SHARES AND STATED VALUE OF CUMULATIVE
REDEEMABLE PREFERRED STOCK, SERIES C. There is hereby authorized and established
a series of Preferred Stock that shall be designated as "Cumulative Redeemable
Preferred Stock, Series C" (hereinafter referred to as "Series C Preferred"),
and the number of shares constituting such series shall be Forty-Five Thousand
(45,000). Such number of shares may be increased or decreased, but not to a
number less than the number of shares of Series C Preferred then issued and
outstanding, by resolution adopted by the full Board of Directors. The "Stated
Value" per share of the Series C Preferred shall be equal to One Thousand
Dollars ($1,000) subject to adjustments as provided herein.

     Section 2. DEFINITIONS. In addition to the definitions set forth elsewhere
herein, the following terms shall have the meanings indicated:

     ADJUSTED CURRENT LIABILITIES: shall mean, (a) the total of all items which
would appear as a current liability upon a balance sheet of the Corporation or
its consolidated subsidiaries prepared in accordance with GAAP, less (b) the
total of any such items appearing as a current liability which would be included
in the definition of Total Consolidated Indebtedness.


<PAGE>   2



     ADJUSTED NET WORKING CAPITAL: shall mean (a) the total of all items which
would appear as current assets upon a balance sheet of the Corporation or its
consolidated subsidiaries prepared in accordance with GAAP less (b) Adjusted
Current Liabilities.

     BUSINESS DAY: means any day other than a Saturday, Sunday or a day on which
banking institutions in Houston, Texas are authorized or obligated by law or
executive order to close.

     CALCULATION DATE: means any date on which PV-10 Value (defined below) is
calculated, as follows: (i) PV-10 Value shall be calculated by independent
reserve engineers (designated by the Corporation and reasonably acceptable to
the holders of a majority of the Series C Preferred outstanding at such time) as
of each January 1, the final report for which shall be provided to the
Corporation and the holders of Series C Preferred no later than the following
March 16, (ii) PV-10 Value shall be calculated by the Corporation's reserve
engineers as of each July 1, commencing in 2001, the final report for which
shall be provided to the Corporation and the holders of Series C Preferred no
later than the following August 14, and (iii) PV-10 Value shall be calculated by
independent reserve engineers (designated by the holders of a majority of the
Series C Preferred outstanding and reasonably acceptable to the Corporation) as
of a date other than January 1 or July 1, as requested by the holders of a
majority of the Series C Preferred outstanding; provided, however, that no
Calculation Date shall occur prior to September 1, 2000. The costs and expenses
of each such report contemplated under this definition shall be borne by the
Corporation; provided, that if a report is requested and prepared under clause
(iii) of this definition more than once during any given calendar year, the
costs and expenses of the second and any subsequent report requested and
prepared during such year shall be borne by the holders of the Series C
Preferred outstanding, pro rata based on their then respective ownership of the
shares of Series C Preferred outstanding.

     CAPITALIZED LEASE OBLIGATION: means any obligation to pay rent or other
amounts under a lease of (or other agreement conveying the right to use) any
property (whether real, personal or mixed) that is required to be classified and
accounted for as a capital lease obligation under GAAP (defined below), and, for
the purpose of this designation, the amount of such obligation at any date shall
be the capitalized amount thereof at such date, determined in accordance with
GAAP.

     CHANGE OF CONTROL: means (i) any merger, reorganization, purchase or sale
of voting securities, or other transaction resulting in at least fifty percent
50% of the issued and outstanding shares of voting securities of the Corporation
outstanding immediately prior to the consummation of such transaction being
"beneficially owned" by a single Person or a "group," as such terms are defined
in Rule 13d-3 and 13d-5, respectively, promulgated by the Securities and
Exchange Commission under the Securities Exchange Act of 1934, as amended, (ii)
a sale, in one or more related transactions, of substantially all the assets of
the Corporation, or (iii) the time at which Tim Goff has ceased to serve as the
Chief Executive Officer of the Corporation for a period of 30 consecutive days;
provided that, the following shall not be deemed a Change of Control: (a) the
acquisition or beneficial ownership of voting securities by the Initial Holders,
their respective affiliates, or any group of which an Initial Holder or their
respective affiliates is a member; (b) any repurchase of voting securities by
the Corporation or any subsidiary of the Corporation; (c) any transaction
pursuant to which securities are transferred by an Initial Holder

<PAGE>   3

or an affiliate of an Initial Holder; (d) any transaction that causes a Person
to become the beneficial owner of voting securities of the Corporation as a
result of acquiring an interest in an Initial Holder, an affiliate of an Initial
Holder or a transferee of an Initial Holder, or (e) any distribution or dividend
to equity-holders made by any of the following entities: BEC Partnership, a
Texas general partnership, TJG Investments, Inc., a Texas corporation, BOC
Operating Corporation, a Texas corporation, and BER Partnership L.P., a Texas
limited partnership.

     COMMON STOCK: means the common stock, $.01 par value per share, of the
Corporation.

     EXCESS OFFERING PROCEEDS: means, with respect to any Qualified Public
Offering (defined below), the lesser of (i) the net proceeds received by the
Corporation from such offering (less discounts, commissions and costs directly
incurred by the Corporation in connection with the offering) and (ii) the amount
of Series C Preferred and Parity Securities that the Corporation may redeem in
compliance with all loan agreements, mortgages, indentures, guarantees, or other
evidences of indebtedness to which the Corporation is subject on the date of the
closing of such offering.

     GAAP: means generally accepted accounting principles, consistently applied,
that are set forth in the opinions and pronouncements of the Accounting
Principles Board of the American Institute of Certified Public Accountants and
statements and pronouncements of the Financial Accounting Standards Board or in
such other statements by such other entity as may be approved by a significant
segment of the accounting profession of the United States of America.

     INITIAL HOLDERS: means Energy Capital Investment Company PLC, an English
investment company, EnCap Energy Capital Fund III-B, L.P., a Texas limited
partnership, BOCP Energy Partners, L.P., a Texas limited partnership, EnCap
Energy Capital Fund III, L.P., a Texas limited partnership, Kayne Anderson
Energy Fund, L.P., a Delaware limited partnership, BancAmerica Capital Investors
SBIC I, L.P.. a Delaware limited partnership, Eos Partners, L.P., a Delaware
limited partnership, Eos Partners SBIC, L.P., a Delaware limited partnership,
Eos Partners SBIC II, L.P., a Delaware limited partnership, SGC Partners II LLC,
a Delaware limited liability company, and Bankers Trust Company, a New York
banking corporation.

     JUNIOR SECURITIES: means the Common Stock, any preferred stock of the
Corporation issued and outstanding on the Original Issue Date (other than the
"Cumulative Redeemable Preferred Stock, Series B" ("Series B Preferred")), or
any other series of stock issued by the Corporation ranking junior as to the
Series C Preferred with respect to payment of dividends, or upon liquidation,
dissolution or winding up of the Corporation.

     ORIGINAL ISSUE DATE: means the date on which shares of the Series C
Preferred are first issued.

     PARITY SECURITY: means the Series B Preferred or any other class or series
of stock issued by the Corporation ranking on a parity with the Series C
Preferred with respect to payment of dividends, and upon liquidation,
dissolution or winding up of the Corporation.


<PAGE>   4

     PERSON: means any individual, corporation, association, partnership, joint
venture, limited liability company, trust, estate, or other entity or
organization, other than the Corporation, any subsidiary of the Corporation, any
employee benefit plan of the Corporation or any subsidiary of the Corporation,
or any entity holding shares of Common Stock for or pursuant to the terms of any
such plan.

     PREFERRED STOCK REDEMPTION VALUE: on any Calculation Date shall equal (i)
the number of shares of a series of Preferred Stock outstanding on the
Calculation Date, multiplied by the Stated Value of the series of Preferred
Stock, plus (ii) all accrued but unpaid dividends on the Calculation Date.

     PROVED RESERVES: means "Proved Reserves" as defined in the Definitions for
Oil and Gas Reserves promulgated by the Society of Petroleum Engineers (or any
generally recognized successor) as in effect at the time in question.

     PV-10 VALUE: means the present value, discounted at 10% per annum, of the
future net cash flow attributable to the Corporation's and its subsidiaries'
estimated Proved Reserves. Future cash flows will be calculated using (i) prices
based upon the average of the pricing assumptions then being utilized by the
three largest banks in Houston, Texas, actively involved in energy lending, (ii)
costs and production taxes derived from and consistent with those actually
incurred by the Corporation, escalated at the same rate, if any, being applied
to prices, and (iii) such other assumptions as shall be reasonably acceptable to
the holders of a majority of the Series C Preferred.

     QUALIFIED PUBLIC OFFERING: means a public offering for cash by the
Corporation of securities pursuant to a registration statement declared
effective by the Securities and Exchange Commission under the Securities Act of
1933, as amended, other than an offering on Form S-8 or successor form thereof.

     REDEMPTION DATE: means the date fixed for any redemption of the Series C
Preferred as provided in Section 5 or 6.

     REDEMPTION PRICE: means, for each share of Preferred Stock on any
Redemption Date, the Stated Value of such share plus all accrued and unpaid
dividends on such share to and including such Redemption Date.

     SENIOR SECURITIES: means any class or series of stock issued by the
Corporation ranking senior to the Series C Preferred with respect to payment of
dividends, or upon liquidation, dissolution or winding up of the Corporation.

     TOTAL CONSOLIDATED INDEBTEDNESS: means without duplication, (a) all
liabilities of the Corporation and its consolidated subsidiaries for borrowed
money or for the deferred purchase price of property or services (excluding any
trade accounts payable and other accrued current liabilities incurred in the
ordinary course of business), and all liabilities of such persons incurred in
connection with any letters of credit, bankers' acceptances or other similar
credit transactions or any agreement to purchase, redeem, exchange, convert or
otherwise acquire for value any


<PAGE>   5

capital stock, or any warrants, rights or options to acquire capital stock
outstanding, if, and to the extent, any of the foregoing would appear as a
liability upon a balance sheet of such Person prepared in accordance with GAAP,
(b) all obligations of the Corporation and its consolidated subsidiaries
evidenced by bonds, notes, debentures or other similar instruments, if, and to
the extent, any of the foregoing would appear as a liability upon a balance
sheet prepared in accordance with GAAP, (c) all indebtedness of the Corporation
and its consolidated subsidiaries created or arising under any conditional sale
or other title retention agreement with respect to property acquired (even if
the rights and remedies of the seller or lender under such agreement in the
event of default are limited to repossession or sale of such property), but
excluding trade accounts payable arising in the ordinary course of business
unless and until such accounts payable are outstanding more than 90 days, (d)
all Capitalized Lease Obligations, (e) all indebtedness referred to in the
preceding clauses of other Persons, the payment of which is secured by (or for
which the holder of such indebtedness has an existing right to be secured by)
any lien upon property (including, without limitation, accounts and contract
rights) owned by the Corporation or its subsidiaries (the amount of such
obligation being deemed to be the lesser of the value of such property or the
amount of the obligation so secured), (f) all guarantees by the Corporation and
its subsidiaries of indebtedness referred to in this definition, and (g) to the
extent not otherwise included in Adjusted Current Liabilities or any of the
foregoing clauses of this definition of Total Consolidated Indebtedness, all
amounts (including damages, fines, penalties, and interest thereon) owed by the
Corporation and its subsidiaries pursuant to a final, nonappealable judgment
rendered by a court or other governmental body. Notwithstanding the foregoing,
the amounts accrued to redeem the Series B Preferred or Series C Preferred or
representing dividends or other amounts payable on or with respect to the Series
B Preferred or the Series C Preferred shall not be deemed Total Consolidated
Indebtedness.

     TOTAL PROVED COVERAGE: means, on any Calculation Date, (i) the PV-10 Value
plus the lesser of (a) Adjusted Net Working Capital (or minus such amount if
negative) or (b) the total of all items which would appear as cash and cash
equivalents upon a balance sheet of the Corporation or its consolidated
subsidiaries prepared in accordance with GAAP plus (only to the extent not
already included in cash and cash equivalents under this clause (b)) all amounts
in escrow or on deposit that are transferred by the Corporation in connection
with a pending acquisition divided by (ii) the sum of (x) Total Consolidated
Indebtedness plus (y) the Preferred Stock Redemption Value for the Series B
Preferred Stock on such date plus (z) the Preferred Stock Redemption Value for
the Series C Preferred Stock on such date.

<PAGE>   6

     Section 3. DIVIDENDS AND DISTRIBUTIONS.

     (a) The Series C Preferred shall rank prior to the Junior Securities with
respect to dividends. The holders of shares of the Series C Preferred shall be
entitled to receive, when, as and if declared by the Board of Directors, as
legally available, cumulative dividends. The rate of dividends per share shall
be expressed as a percentage of the Stated Value in effect at the relevant time
("Dividend Rate") and shall initially be 12% per annum; provided, however, that
the Dividend Rate shall be reset as of each Calculation Date as follows: (i) if
the Total Proved Coverage on such Calculation Date is 1.5 or greater, then the
Dividend Rate for the period commencing on such Calculation Date and ending on
the day immediately prior to the next succeeding Calculation Date shall be 12%
per annum; but (ii) if the Total Proved Coverage on such Calculation Date is
less than 1.5, then the Dividend Rate for the period commencing on such
Calculation Date and ending on the day immediately before the next Calculation
Date shall be 15% per annum. However, if on any Calculation Date -- following
the first Calculation Date - (the "Measuring Date") it is the case that (a) the
Dividend Rate was at least 15% on the day before such Measuring Date, and (b)
the Total Proved Coverage is less than 1.5 on the Measuring Date, and (c) the
Total Proved Coverage was less than 1.5 on the most immediately preceding
Calculation Date that also is at least 180 days prior to the Measuring Date,
then the Dividend Rate for the period commencing on the Measuring Date and
ending on the day immediately before the next Calculation Date shall be 18% per
annum. Such dividends on shares of Series C Preferred shall be cumulative from
the date such shares are issued, whether or not in any period the Corporation
shall be legally permitted to make the payment of such dividends and whether or
not such dividends are declared, and shall be payable when, as and if declared
by the Board of Directors in cash on each January 1, April 1, July 1, and
October 1, in each year, except that if any such date is not a Business Day then
such dividends shall be payable on the next succeeding Business Day (as
applicable, each a "Dividend Payment Date"). Subject to the last sentence of
this subsection (a), cash dividends shall accrue and be payable at the Dividend
Rate in effect as of the immediately preceding Calculation Date. Such dividends
shall accrue whether or not there shall be (at the time such dividend becomes
payable or at any other time) profits, surplus or other funds of the Corporation
legally available for the payment of dividends.

     (b) Dividends shall be calculated on the basis of the time elapsed from and
including the date of issuance of such shares to and including the Dividend
Payment Date or on any final distribution date relating to conversion or
redemption or to a dissolution, liquidation or winding up of the Corporation.
Dividends payable on the shares of Series C Preferred for any period of less
than a full calendar year shall be prorated for the partial year on the basis of
a 360-day year of 12 30-day months..

     (c) To the extent dividends are not paid on a Dividend Payment Date, all
dividends which shall have accrued on each share of Series C Preferred
outstanding as of such Dividend Payment Date shall, for purposes of calculating
dividends thereon, be added to the Stated Value of such share of Series C
Preferred and shall remain a part thereof until paid, and dividends shall accrue
at the Dividend Rate and be paid on such share of Series C Preferred on the
basis of the Stated Value, as so adjusted. No interest, or sum of money in lieu
of interest, shall be payable in respect of any dividend payment or payments on
the Series C Preferred which are in arrears.


<PAGE>   7

     (d) Dividends payable on each Dividend Payment Date shall be paid to record
holders of the shares of Series C Preferred as they appear on the books of the
Corporation at the close of business on the tenth Business Day immediately
preceding the respective Dividend Payment Date or on such other record date as
may be fixed by the Board of Directors of the Corporation in advance of a
Dividend Payment Date, provided that no such record date shall be less than ten
nor more than sixty calendar days preceding such Dividend Payment Date.
Dividends in arrears may be declared and paid at any time to holders of record
on a date not more than 60 days preceding the payment date as may be fixed by
the Board of Directors. Dividends paid on shares of Series C Preferred in an
amount less than the total amount of such dividends at the time payable shall be
allocated pro rata on a share by share basis among all shares outstanding.

     (e) So long as any shares of Series C Preferred are outstanding, no
dividend or other distribution, whether in liquidation or otherwise, shall be
declared or paid, or set apart for payment on or in respect of, any Junior
Securities, nor shall any Junior Securities be redeemed, purchased or otherwise
acquired for any consideration prior to the stated maturity thereof (or any
money be paid to a sinking fund or otherwise set apart for the purchase or
redemption of any such Junior Securities), without the prior consent of the
holders of a majority of the outstanding shares of Series C Preferred voting
together as a separate class. So long as any shares of Series C Preferred are
outstanding and without the prior consent of the holders of a majority of the
outstanding shares of Series C Preferred voting together as a separate class, no
dividend or other distribution, whether in liquidation or otherwise, shall be
declared or paid, or set apart for payment on or in respect of, any Parity
Securities, nor shall any Parity Securities be redeemed, purchased or otherwise
acquired for any consideration prior to the stated maturity thereof (or any
money be paid to a sinking fund or otherwise set apart for the purchase or
redemption of any such Parity Securities), unless (i) if there are any accrued
and unpaid dividends on the Series C Preferred Stock or such Parity Stock, such
dividend or distribution shall be allocated to pay such accrued and unpaid
dividends the Series C Preferred and such Parity Stock, pro rata based on the
amount of such accrued and unpaid dividends and (ii) if all accrued and unpaid
dividends have been paid on the Series C Preferred and such Parity Stock, such
dividends and distributions shall be allocated pro rata to the holders of the
Series C Preferred and the Parity Stock based on the respective liquidation
preferences thereof.

     Section 4. LIQUIDATION PREFERENCE.

     (a) In the event of any liquidation, dissolution or winding up of the
Corporation (in connection with the bankruptcy or insolvency of the Corporation
or otherwise), whether voluntary or involuntary, before any payment or
distribution of the assets of the Corporation (whether capital or surplus) shall
be made to or set apart for the holders of shares of any Junior Securities, the
holders of the shares of Series C Preferred shall be entitled to receive an
amount per share equal to the Stated Value per share held by them, plus all
accrued and unpaid dividends on each share. To the extent the available assets
are insufficient to fully satisfy such amounts, then the holders of the Series C
Preferred shall share ratably in such distribution in the proportion that each
holder's shares bears to the total number of shares of Series B Preferred and
Series C Preferred outstanding. No further payment on account of any such
liquidation, dissolution or winding up of the Corporation shall be paid to the
holders of the shares of Series C Preferred or


<PAGE>   8

the holders of any Parity Securities unless there shall be paid at the same time
to the holders of the shares of Series C Preferred and the holders of any Parity
Securities proportionate amounts determined ratably in proportion to the full
amounts to which the holders of all outstanding shares of Series C Preferred and
the holders of all such outstanding Parity Securities are respectively entitled
with respect to such distribution. For purposes of this Section 4, a
consolidation or merger of the Corporation with one or more partnerships,
corporations or other entities or a sale, lease, exchange or transfer of all or
any substantial part of the Corporation's assets for cash, securities or other
property shall be deemed to be a liquidation, dissolution or winding-up of the
Corporation, whether voluntary or involuntary.

     (b) After the payment of the full amount to the holders of Series C
Preferred pursuant to the preceding paragraph, and subject to the rights of
holders of Junior Securities other than the Common Stock, the holders of Common
Stock shall share ratably in the distribution of the remaining available assets
of the Corporation, in the proportion that each holder's shares of Common Stock,
bears to the total number of shares of Common Stock of the Corporation
outstanding.

     (c) Written notice of any liquidation, dissolution or winding up of the
Corporation, stating the payment date or dates when and the place or places
where the amounts distributable in such circumstances shall be payable, shall be
given by first class mail, postage prepaid, not less than fifteen days prior to
any payment date stated therein, to the holders of record of the shares of
Series C Preferred at their respective addresses as the same shall appear in the
records of the Corporation.

     Section 5. OPTIONAL REDEMPTION BY THE CORPORATION. The outstanding shares
of Series C Preferred are subject to redemption in accordance with the following
provisions:

     (a) Subject to the terms hereof, the Corporation may at its option elect to
redeem the outstanding shares of Series C Preferred in multiples of not less
than One Million Dollars ($1,000,000), until such time as the aggregate
Redemption Price of the Outstanding Series C Preferred is $25,000,000;
thereafter, any redemption under this Section 5 at the election of the
Corporation must be of all shares of Series C Preferred then outstanding. The
number of shares redeemed under this Section 5 shall be allocated among the
holders of Series C Preferred according to, as measured on the date of the
notice required by Section 5(c) below, the relative number of shares owned by
each holder as compared to the total number of issued and outstanding shares of
Series C Preferred.

     (b) The redemption price per share for Series C Preferred redeemed on any
optional Redemption Date shall be the Redemption Price. Subject to Section 5(c)
hereof, the aggregate Redemption Price on all shares shall be paid in cash from
any source of funds legally available therefor.

     (c) Not less than thirty nor more than sixty days prior to the Redemption
Date fixed for any redemption of any shares of Series C Preferred under this
Section 5, a notice specifying the Redemption Date and place of such redemption
shall be given by first class mail, postage prepaid, to the holders of record of
the shares of Series C Preferred to be redeemed at their

<PAGE>   9

respective addresses as the same shall appear on the books of the Corporation,
calling upon each such holder of record to surrender to the Corporation on the
Redemption Date at the place designated in such notice the holder's certificate
or certificates representing the number of shares of Series C Preferred
designated for redemption from such holder. On or after the Redemption Date,
each holder of shares of Series C Preferred called for redemption shall
surrender his certificate or certificates for such shares to the Corporation at
the place designated in the redemption notice and shall thereupon be entitled to
receive payment of the aggregate Redemption Price for such shares. From and
after the Redemption Date, unless there shall have been a default in payment of
the Redemption Price, all rights of the shares of Series C Preferred designated
for redemption (except the right to receive the Redemption Price without
interest upon Surrender of the related certificate or certificates) shall cease
with respect to such shares, and such shares shall not thereafter be transferred
on the books of the Corporation or be deemed to be outstanding for any purpose
whatsoever.

     Section 6. MANDATORY REDEMPTION; PUT RIGHT.

     (a) As soon as possible following (i) the sixth anniversary of the Original
Issue Date, or (ii) a Change of Control, the Corporation shall redeem each
Series C Preferred share for cash for the Redemption Price.

     (b) Following the closing of a Qualified Public Offering, the Corporation
shall redeem for cash, in the manner provided for in subsection (c), a number of
shares of Series C Preferred calculated by dividing the Series C Excess Offering
Proceeds by the Redemption Price. The Series C Excess Offering Proceeds shall
equal the Excess Offering Proceeds multiplied by a fraction the numerator of
which is the aggregate Stated Value plus accrued and unpaid dividends of the
Series C Preferred and the denominator of which is the aggregate Stated Value
plus accrued and unpaid dividends of the Series C Preferred plus the aggregate
Stated Value plus accrued and unpaid dividends of the Series B Preferred. If the
number of shares of Series C Preferred which the Corporation is able to purchase
with the Excess Offering Proceeds is less than the aggregate number of shares
then outstanding, the Corporation shall redeem shares from each holder of Series
C Preferred pro rata based on the number of shares of Series C Preferred owned
by such holder. In either case, the price paid for each share redeemed under
this subsection (b) shall be the Redemption Price.

     (c) Not less than thirty nor more than sixty days prior to the Redemption
Date fixed for any redemption of any shares of Series C Preferred under Section
6(a) or (b) (or, if no date can be predetermined, then not later than five days
following the consummation of a Qualified Public Offering or Change of Control),
a notice specifying the mandatory Redemption Date and place of such redemption
shall be given by first class mail, postage prepaid, to the holders of record of
the shares of Series C Preferred at their respective addresses as the same shall
appear on the books of the Corporation, calling upon each such holder of record
to surrender to the Corporation on the mandatory Redemption Date at the place
designated in such notice the holder's certificate or certificates representing
the number of shares of Series C Preferred owned by such holder and being
redeemed on such mandatory Redemption Date. On or after the mandatory Redemption
Date, each holder of shares of Series C Preferred shall surrender his
certificate or certificates for such shares to the Corporation at the place and
amount designated in

<PAGE>   10

the redemption notice and shall thereupon be entitled to receive payment of the
aggregate Redemption Price for such shares. From and after the mandatory
Redemption Date, unless there shall have been a default in payment of the
Redemption Price, all rights of the shares of Series C Preferred being redeemed
(except the right to receive the Redemption Price without interest upon
surrender of the related certificate or certificates) shall cease, and such
shares shall not thereafter be transferred on the books of the Corporation or be
deemed to be outstanding for any purpose whatsoever.

     (d) If, at any time after the third anniversary of the Original Issue Date,
the Company fails to fully make a then-current dividend payment in cash (not
including amounts representing accrued and unpaid dividends up to the third
anniversary of the Original Issue Date) at the end of any calendar quarter, then
the holders of shares of Series C Preferred (as approved by the holders of at
least two-thirds of the outstanding shares of Series C Preferred), shall have
the option to require the Corporation to redeem each outstanding share of Series
C Preferred for cash at the Redemption Price. In the event such option is
exercised, all holders of Series C Preferred shall deliver the certificates
representing the shares of Series C Preferred to the Corporation and a notice of
the election of the holders to have all of such shares redeemed. Upon receipt of
such certificate and notice, the Corporation shall, subject to any applicable
restrictions of law or regulations, promptly redeem the shares for which such
holders have elected to be redeemed and pay to or on the order of such holders
in immediately available funds the full Redemption Price for each share of
Series C Preferred then outstanding.

     (e) In connection with a redemption under Section 6(a) or (d), if the
Corporation has insufficient funds (whether by legal prohibition or otherwise)
to initially redeem all shares required to be redeemed thereunder, then the
Corporation shall from time to time whenever possible use the maximum amount of
funds available (until all shares of Series C Preferred are redeemed), and in
each partial redemption the number of shares redeemed and the redemption price
therefor shall be allocated according to the relative number of Series C
Preferred shares owned by each holder as compared to the total number of shares
of Series C Preferred outstanding at such time.

     Section 7. REACQUIRED SHARES. Any shares of Series C Preferred repurchased,
redeemed, converted or otherwise acquired by the Corporation shall be retired
and canceled promptly after the acquisition thereof. All such shares shall upon
their cancellation become authorized but unissued shares of Preferred Stock,
without designation as to series, and may thereafter be reissued.

     Section 8. VOTING RIGHTS.

     (a) Except as otherwise provided in this Section 8 or required by law or
any provision of the Articles of Incorporation of the Corporation, the shares of
Series C Preferred shall not confer any voting rights.



<PAGE>   11



     (b) For so long as any shares of Series C Preferred remain issued and
outstanding, the Corporation shall not, without the affirmative vote or consent
of the holders of a majority of the shares of Series C Preferred then
outstanding, voting together as a separate class: (i) authorize, create or
issue, or increase the authorized or issued amount of, any class or series of
capital stock, or any security convertible into or exchangeable for shares of
capital stock or reclassify or modify any Junior Securities so as to become
Parity Securities or Senior Securities; (ii) amend, repeal or change any of the
provisions of the Articles of Incorporation of the Corporation (including the
Certificate of Designations relating to the Series C Preferred), (iii) authorize
or take any action resulting in the merger, reorganization, change of control,
conversion, or sale of all or substantially all of the assets of the
Corporation; (iv) redeem, repurchase or otherwise reacquire any shares of a
class or series of Junior Securities or Parity Securities (other than
redemptions from employees of the Corporation in connection with their
employment termination); (v) authorize or take any action resulting in a
transaction between the Corporation and one of its affiliates (other than a
wholly-owned subsidiary), unless on terms no less favorable than would have been
available with either a less than wholly-owned subsidiary of the Corporation or
an independent third party; or (vi) increase or decrease the size of the Board
of Directors.

     Section 9. RECORD HOLDERS. The Corporation may deem and treat the record
holder of any shares of Series C Preferred as the true and lawful owner thereof
for all purposes, and the Corporation shall not be affected by any notice to the
contrary.

     Section 10. NOTICE. Except as may otherwise be provided by law or provided
for herein, all notices referred to herein shall be in writing, and all notices
hereunder shall be deemed to have been given upon receipt upon the earlier of
receipt of such notice or three Business Days after the mailing of such notices
sent by Registered Mail (unless first-class mail shall be specifically permitted
for such notice under the terms hereof) with postage prepaid, addressed: If to
the Corporation, to its principal executive offices (Attention: Corporate
Secretary) or to any agent of the Corporation designated as permitted hereby; or
if to a holder of the Series C Preferred, to such holder at the address of such
holder of the Series C Preferred as listed in the stock record books of the
Corporation, or to such other address as the Corporation or holder as the case
may be, shall have designated by notice similarly given.

     Section 11. SUCCESSORS AND TRANSFEREES. The provisions applicable to shares
of Series C Preferred shall bind and inure to the benefit of and be enforceable
by the Corporation, the respective successors to the Corporation, and by any
record holder of shares of Series C Preferred.

     Section 12. DENIAL OF PREEMPTIVE RIGHTS. The Series C Preferred is not
entitled to any preemptive or subscription right in respect of any securities of
the Corporation.

     RESOLVED FURTHER, that the appropriate officers of the Corporation be, and
they are hereby, authorized and directed from time to time to execute such
certificates, instruments or other documents and do all such things as may be
necessary, or advisable in their discretion in order to carry out the terms
hereof, including the filing with the Secretary of State for the State of Texas
of a copy of the foregoing resolution executed by an officer of the Corporation.


Dated: March __, 2000

                                        BARGO ENERGY COMPANY


                                        ---------------------------------
                                        Jonathan M. Clarkson
                                        President