<PAGE>   1
                                                                     EXHIBIT 4.2

                           CERTIFICATE OF DESIGNATIONS

                                     of the

                      SERIES B CONVERTIBLE PREFERRED STOCK

                                       of

                              ENERGY PARTNERS, LTD.

                         Pursuant to Section 151 of the
                General Corporation Law of the State of Delaware


         Energy Partners, Ltd., a Delaware corporation (the "COMPANY"), HEREBY
CERTIFIES that, pursuant to authority conferred upon the Board of Directors of
the Company by the Restated Certificate of Incorporation of the Company and in
accordance with the provisions of Section 151 of the General Corporation Law of
the State of Delaware, the Board of Directors of the Company duly adopted a
resolution providing for the issuance of a new series of preferred stock
designated as the Series B Convertible Preferred Stock, which resolution is as
follows:

         RESOLVED, that a series of the Company's preferred stock, par value
$1.00 per share, designated as the Series B Convertible Preferred Stock be and
hereby is created and that the voting powers, designations, preferences, and
relative, participating, optional or other special rights thereof, and the
qualifications, limitations or restrictions thereof be as follows:

                      SERIES B CONVERTIBLE PREFERRED STOCK

         SECTION 1. CERTAIN DEFINITIONS. The following terms shall have the
following meanings:

         "ADDITIONAL SHARES OF COMMON STOCK" shall mean all shares of Common
Stock issued by the Company after the Closing Date, other than: (a) shares of
Common Stock issued or issuable to officers, directors or employees of, or
consultants to, the Company or its subsidiaries pursuant to any employee stock
incentive program or agreement approved by a majority of the Evercore Directors;
(b) shares of Common Stock issued or issuable upon conversion of shares of the
Preferred Stock or the Series A Preferred Stock; (c) shares of Common Stock
issued or issuable as a dividend or other distribution on the Preferred Stock or
the Series A Preferred Stock; (d) Warrant Shares, (e) Escrow Shares, (f) Bonus
Shares, (g) shares of Common Stock issued or issuable pursuant to an acquisition
approved by the majority of the Evercore Directors of another corporation by
merger, purchase of substantially all of the assets, or other reorganization;
and (h) shares of Common Stock issued or issuable in a transaction described in
Section 6.3(a).



                                       -1-
<PAGE>   2

         "BONUS SHARES" means the number of shares of Common Stock issued
pursuant to Section 8.2 of the Stockholder Agreement.

         "CLOSING DATE" means the date of the closing of the first sale of the
Preferred Stock pursuant to the Stock Purchase Agreement.

         "COMMON STOCK" means the Company's common stock, no par value.

         "COMPUTATION DATE" means the earlier of (i) the date on which the
Company shall enter into a firm contract for the issuance of Common Stock,
warrants, options or other rights or Convertible Securities and (ii) the date of
actual issuance of Common Stock, warrants, options or other rights, or
Convertible Securities.

         "CONVERSION PRICE" means $9,747.79, as adjusted from time to time as
set forth in Section 6.3.

         "CONVERTIBLE SECURITIES" means evidences of indebtedness, shares of
capital stock or other securities which are convertible into or exchangeable for
Additional Shares of Common Stock.

         "DEEMED ARREARAGE VALUE" of a share of Preferred Stock means (a) an
amount in cash equal to either (i) the cash dividend or (ii) $100 multiplied by
the number of whole or fractional Dividend Shares, as applicable, accrued at the
Dividend Rate on such share during the partial Dividend Period ending on the
date of conversion, the date fixed for redemption or the date of payment upon
liquidation, as the case may be, and (b) if one or more dividends has accrued
and has not been paid on such share, an amount in cash equal to $100 multiplied
by the number of whole and fractional Dividend Shares that would have been
issued as dividends on such share and on such Dividend Shares prior to the
Trigger Date, together with the aggregate amount of cash dividends actually
accrued and cash dividends that would have accrued after the Trigger Date on
such Dividend Shares to the date of conversion, the date fixed for redemption or
the date of payment upon liquidation, as the case may be.

         "DIVIDEND ACCRUAL DATE" has the meaning given such term in Section 3.1.

         "DIVIDEND PAYMENT DATE" has the meaning given such term in Section 3.1.

         "DIVIDEND PERIOD" has the meaning given such term in Section 3.1.

         "DIVIDEND RATE" means 10% per annum.

         "DIVIDEND SHARES" means fully paid and nonassessable shares, or
fractions thereof, of Preferred Stock paid as dividends on Preferred Stock
pursuant to Section 3.2(a).



                                       -2-
<PAGE>   3

         "ESCROW SHARES" means the number of shares of Common Stock released
from escrow in accordance with Section 7.1 of the Stockholder Agreement.

         "EVERCORE DIRECTORS" means any directors of the Company designated,
nominated or elected by the Evercore Entities pursuant to Section 3.2 of the
Stockholder Agreement.

         "EVERCORE ENTITIES" has the meaning given such term in the Stockholder
Agreement.

         "FAIR MARKET PRICE" of a share of Common Stock means on any particular
date (a) the last sales price per share of the Common Stock on such date on the
principal stock exchange on which the Common Stock has been listed or, if there
is no such price on such date, then the last price on such exchange on the date
nearest preceding such date, (b) if the Common Stock is not listed on any stock
exchange, the final bid price for a share of Common Stock in the
over-the-counter market, as reported by the Nasdaq Stock Market at the close of
business on such date, or the last sales price if such price is reported and
final bid prices are not available, (c) if the Common Stock is not quoted on the
Nasdaq Stock Market, the final bid price for a share of Common Stock in the
over-the-counter market as reported by the National Quotations Bureau
Incorporated (or any similar organization or agency succeeding to its functions
of reporting prices), or (d) if the Common Stock is not publicly traded, as
determined by a nationally recognized investment banking firm selected in good
faith by the Board of Directors of the Company (other than directors designated
for nomination by holders of the Preferred Stock or their successors under the
Stockholder Agreement) and approved by the holders of a majority of the
Preferred Stock, which approval will not unreasonably be withheld; provided,
that none of the transactions related to the foregoing shall include purchases
by any "affiliate" (as such term is defined in the General Rules and Regulations
under the Securities Act of 1933) of the Company.

         "FLOOR PRICE" means $14,073.98 prior to the Trigger Date. As of the
Trigger Date and for any day thereafter, "FLOOR PRICE" means the number obtained
by the following formula:

<TABLE>
<S>                    <C>
         Floor Price = Implied Value + (Warrant Shares x 9,747.79)
                       -------------------------------------------------------
                       5,642.3 + Escrow Shares + Bonus Shares + Warrant Shares

         "IMPLIED VALUE" means the number obtained by the following formula:

                       60,000,000  x  [2,826.8 + Escrow Shares + Bonus Shares                  ]
                                      ----------------------------------------------------------
                                      [12,042.3 + Escrow Shares + Bonus Shares + Warrant Shares]
         Implied Value = -----------------------------------------------------------------------
                       .501        -  [2,826.8 + Escrow Shares + Bonus Shares                  ]
                                      ----------------------------------------------------------
                                      [12,042.3 + Escrow Shares + Bonus Shares + Warrant Shares]
</TABLE>

         "JUNIOR STOCK" means the Common Stock and any and all classes or series
of capital stock of the Company over which shares of Preferred Stock have a
preference as to distribution of assets on any liquidation of the Company.



                                       -3-
<PAGE>   4

         "PARITY STOCK" means the Series A Preferred Stock and the Series C
Preferred Stock and any and all other classes or series of capital stock of the
Company ranking as to distribution of assets on any liquidation of the Company
on parity with the Preferred Stock.

         "PREFERRED STOCK" has the meaning given such term in Section 2 hereof.

         "QUALIFYING PUBLIC OFFERING" has the meaning given such term in the
Stockholder Agreement.

         "REPORT REVIEW DATE" means the date that is 30 days following the
delivery date of the Reserve Report relating to the Company's reserves at
December 31, 2001.

         "RESERVE REPORT" has the meaning given such term in the Stockholder
Agreement.

         "SERIES A PREFERRED STOCK" means the Series A Convertible Preferred
Stock of the Company established pursuant to resolution of the Board of
Directors on the date hereof.

         "SERIES C PREFERRED STOCK" means the Series C Preferred Stock of the
Company established pursuant to resolution of the Board of Directors on the date
hereof.

         "STOCK PURCHASE AGREEMENT" means that certain Stock Purchase Agreement,
dated as of October 26, 1999, between the Company and Evercore Capital Partners
L.P., Evercore Capital Partners (NQ) L.P. and Evercore Capital Offshore Partners
L.P. as in effect on the date hereof.

         "STOCKHOLDER AGREEMENT" means that certain Stockholder Agreement dated
as of November 17, 1999 among the Company and the stockholders of the Company,
as amended from time to time.

         "TRIGGER DATE" means the Report Review Date, or, at the option of the
holders of the Preferred Stock upon notice to the Company prior to the Report
Review Date, December 31, 2002.

         "VALUATION PROCEDURE" means a determination of fair value of any
securities (other than Common Stock) or property made in good faith by the Board
of Directors (other than directors designated for nomination for holders of the
Preferred Stock or their successors under the Stockholder Agreement); provided,
that if the holders of a majority of the Preferred Stock object to such
determination within 10 days of receipt of written notification thereof, then
the fair value of such property shall be determined in good faith by a
nationally recognized investment banking firm selected in good faith by the
Board of Directors (other than directors designated for nomination by holders of
the Preferred Stock or their successors under the Stockholder Agreement) and
approved by the holders of a majority of the Preferred Stock, which approval
will not unreasonably be withheld.



                                       -4-
<PAGE>   5

         "WARRANT SHARES" means the number of shares of Common Stock issuable
pursuant to the Warrant granted by the Company to Energy Income Fund, L.P. dated
November 17, 1999.

         SECTION 2. DESIGNATION, AMOUNT AND RANKING OF THE PREFERRED STOCK. The
designation of the series of preferred stock created by this resolution shall be
"Series B Convertible Preferred Stock" (the "PREFERRED STOCK"), and the number
of shares constituting this series of Preferred Stock shall be 150,000. Shares
of Preferred Stock shall have the stated value of $100 per share. The Preferred
Stock shall in all respects rank senior in right and priority to the Junior
Stock and equal in right and priority to the Parity Stock, with respect to the
right to receive dividends or other distributions on liquidation, dissolution or
winding up of the Company. The Board of Directors shall authorize additional
shares of Preferred Stock to be available for issuance as dividends if the
number of authorized shares of this series of Preferred Stock is insufficient to
continue accruing or paying Dividend Shares.

         SECTION 3. DIVIDENDS; RESTRICTED PAYMENTS.

         3.1 DIVIDEND PAYMENT.

                  (a) PAYMENT DATES. The holders of the Preferred Stock shall be
entitled to receive, when, as and if declared by the Board of Directors out of
funds legally available for such purpose, dividends payable in accordance with
this Section 3. Dividends on the Preferred Stock shall be cumulative and shall
accrue quarterly in arrears on March 31, June 30, September 30 and December 31
(each, a "DIVIDEND ACCRUAL DATE") of each year (each three-month period (or such
period from the date of original issue until December 31, 1999) expiring on a
Dividend Accrual Date being referred to herein as a "DIVIDEND PERIOD").
Dividends on any shares of the Preferred Stock shall be cumulative and shall
accrue (whether or not declared and whether or not there shall be funds legally
available for the payment of dividends) on and from the date of issue of such
shares of the Preferred Stock; provided, however, that dividends on Dividend
Shares paid in accordance with Section 3.2 shall be cumulative and shall accrue
on and from the Dividend Accrual Date in the Dividend Period in which such
dividend accrued, regardless of when such Dividend Shares were actually issued.
Dividends payable on the Preferred Stock for any period less than a full
Dividend Period shall be computed on the basis of the ratio of the number of
days in such partial period to the actual number of days in such full Dividend
Period. In addition to the cumulative dividend provided for in this Section 3,
if the Company declares a dividend or distribution on the Common Stock, the
holders of shares of Preferred Stock shall be entitled to receive for each share
of Preferred Stock a dividend or distribution in the amount of the dividend or
distribution that would be received by a holder of the Common Stock into which
such share of Preferred Stock is convertible pursuant to Section 6 hereof on the
record date for such dividend or distribution. The date that any dividend shall
be paid pursuant to this Section 3.1 is referred to herein as a "DIVIDEND
PAYMENT DATE."

                  (b) ARREARAGES. Additional dividends shall accrue with respect
to any dividends (including dividends payable pursuant to this sentence) not
paid by the Dividend Accrual Date on which such dividend accrues or in the
manner provided in Section 3.2; such additional dividends



                                       -5-
<PAGE>   6

shall accrue whether or not declared, at the Dividend Rate compounded quarterly,
and shall be payable in the same manner and at such times as provided in Section
3.1 and 3.2 hereof with respect to dividends on each outstanding share of
Preferred Stock.

                  (c) FRACTIONAL SHARES. Each fractional share of Preferred
Stock outstanding or accrued as a Dividend Share, shall be entitled to a ratably
proportionate amount of all dividends accruing with respect to each outstanding
share of Preferred Stock pursuant to Section 3.1 hereof, and all dividends with
respect to such fractional shares shall be fully cumulative and shall accrue
(whether or not declared and whether or not there shall be funds legally
available for the payment of dividends) and shall be payable in the same manner
and at such times as provided for in Sections 3.1 and 3.2 hereof with respect to
dividends on each outstanding share of Preferred Stock.

         3.2 FORM OF PAYMENT.

                  (a) DIVIDEND SHARES. Any dividends accrued on the Preferred
Stock prior to the first Dividend Accrual Date following the Trigger Date shall
when declared be payable by issuing Dividend Shares having an aggregate stated
value equal to the Dividend Rate per share of Preferred Stock on the stated
value of $100.

                  (b) CASH. Any dividends accrued on the Preferred Stock on or
after the first Dividend Accrual Date following the Trigger Date shall when
declared be payable in cash at the Dividend Rate per share of Preferred Stock on
the stated value of $100.

         3.3 RECORD DATE. To the extent permitted by applicable law, the Board
of Directors shall fix a record date for the determination of holders of the
Preferred Stock entitled to receive payment of a dividend declared thereon,
which record date shall be not more than 30 days prior to the applicable
Dividend Payment Date.

         3.4 RESTRICTED PAYMENTS.

                  (a) No dividends shall be declared or paid or set apart for
payment on Parity Stock for any period unless full cumulative dividends have
been or contemporaneously are declared and paid or declared and a sum sufficient
for the payment thereof set apart for such payment on the Preferred Stock for
all Dividend Periods terminating on or prior to the date of payment of such full
cumulative dividends.

                  (b) Unless full cumulative dividends on the Preferred Stock
have been paid prior to or on the date of the declaration of dividends on, or
redemption of, Junior Stock, no dividend shall be declared or paid or set aside
for payment or other distribution declared or made upon the Junior Stock, nor
shall any Junior Stock be redeemed, purchased or otherwise acquired for any
consideration (or any moneys be paid to or made available for a sinking fund for
the redemption of any shares of Junior Stock) by the Company.



                                       -6-
<PAGE>   7

         SECTION 4. REDEMPTION.

         4.1 MANDATORY REDEMPTION. On November 17, 2009, the Company shall
redeem, to the extent it has legally available funds therefor, all shares of
Preferred Stock then outstanding at a redemption price per share equal to the
greater of (a) $100 plus the Deemed Arrearage Value or (b) the Fair Market Price
of the number of shares of Common Stock into which such share of Preferred Stock
is then convertible pursuant to Section 6 hereof; provided, that for purposes of
this Section 4.1, the Fair Market Price shall be calculated as of the close of
business three business days prior to the redemption date. In the case of clause
(a) of the previous sentence, the redemption price shall be paid in cash, and in
the case of clause (b) of the previous sentence, the redemption price shall be
paid by issuing the number of shares of Common Stock into which such share of
Preferred Stock is then convertible pursuant to Section 6 hereof; provided, that
at the option of the holders of the Preferred Stock exercised by notice to the
Company given at least two business days prior to the redemption date, the
redemption price shall be paid in cash at the amount set forth in clause (a) of
the previous sentence if, in the judgment of the holders of the Preferred Stock,
the transaction costs, market risk and uncertainty of liquidating the Common
Stock outweigh the difference in value between (a) and (b). At any time when the
Company shall not have redeemed the full number of shares of Preferred Stock
required to be redeemed pursuant to this Section 4.1, no Parity Stock shall be
redeemed, purchased or otherwise acquired for any consideration (or any moneys
be paid to or made available for a sinking fund for the redemption of any shares
of any Parity Stock) by the Company (except by conversion into or in exchange
for Junior Stock), unless, in the case of the mandatory redemption of,
repurchase of, or fulfillment of a sinking fund obligation in respect of, any
other series of Parity Stock, payments made in respect of the mandatory
redemption of, repurchase of, or fulfillment of a sinking fund obligation in
respect of, the Preferred Stock and all other series of Parity Stock then issued
and outstanding and entitled to such mandatory payments are made pro rata, as
nearly as practicable, so that the amounts of such payments made on the
Preferred Stock and such other series of Parity Stock shall in all cases bear to
each other the same ratio, as nearly as practicable, that such mandatory
payments required to be made on the Preferred Stock and such other series of
Parity Stock bear to each other. The redemption requirements provided hereby
shall be continuous, so that if such requirements cannot be fully discharged,
without further action by any holder of the Preferred Stock, funds legally
available shall be applied therefor until such requirements are fulfilled.

         4.2 OPTIONAL REDEMPTION. From and after the Trigger Date, the Company,
at its option, may redeem shares of Preferred Stock, in whole but not in part,
at any time, at a redemption price per share equal to the greater of (a) $100
plus the Deemed Arrearage Value or (b) the Fair Market Price of the number of
shares of Common Stock into which such share of Preferred Stock is then
convertible pursuant to Section 6 hereof; provided, that for purposes of this
Section 4.2, the Fair Market Price shall be calculated as of the close of
business three business days prior to the redemption date; provided, further,
that the Company may redeem the Preferred Stock in accordance with this Section
4.2 only if the Company simultaneously redeems the Series A Preferred Stock and
the Series C Preferred Stock in whole. In the case of clause (a) of the previous
sentence, the redemption price shall be paid in cash. In the case of clause (b)
of the previous sentence, the redemption price shall be paid by issuing the
number of shares of Common Stock into which such



                                       -7-
<PAGE>   8

share of Preferred Stock is then convertible pursuant to Section 6 hereof;
provided, that at the option of the holders of the Preferred Stock exercised by
notice to the Company given at least two business days prior to the redemption
date, the redemption price shall be paid in cash at the amount set forth in
clause (a) of the previous sentence if, in the judgment of the holders of the
Preferred Stock, the transaction costs, market risk and uncertainty of
liquidating the Common Stock outweigh the difference in value between (a) and
(b).

         4.3 REDEMPTION MECHANICS.

                  (a) At such time as the Company shall redeem shares of
Preferred Stock, notice of such redemption shall be given by first class mail,
postage prepaid, mailed not less than five nor more than 10 days prior to the
redemption date, to each holder of record of the shares to be redeemed, at such
holder's address as the same appears on the stock register of the Company. Each
such notice shall state: (i) the redemption date; (ii) the number of shares of
Preferred Stock to be redeemed; (iii) the redemption price; (iv) the place or
places where certificates for such shares are to be surrendered for payment of
the redemption price; and (v) that dividends on the shares to be redeemed will
cease to accrue on such redemption date.

                  (b) Notice having been mailed as aforesaid, from and after the
redemption date (unless default shall be made by the Company in providing money
for the payment of the redemption price) dividends on the shares of Preferred
Stock so called for redemption shall cease to accrue, said shares shall no
longer be deemed to be outstanding, and all rights of the holders thereof as
stockholders of the Company (except the right to receive from the Company the
redemption price plus the Deemed Arrearage Value to the redemption date) shall
cease. Upon surrender in accordance with said notice of the certificates for any
shares so redeemed (properly endorsed or assigned for transfer, if the Board
shall so require and the notice shall so state), such shares shall be redeemed
by the Company at the redemption price aforesaid.

         4.4 STATUS OF PREFERRED STOCK AFTER REDEMPTION. Any shares of Preferred
Stock that shall at any time have been redeemed or purchased by the Company
shall, after such redemption, have the status of authorized but unissued shares
of Preferred Stock, without designation as to series until such shares are once
more designated as part of a particular series by the Board.

         4.5 RESTRICTIONS ON REDEMPTION. If any dividends on the Preferred Stock
are in arrears, the Company shall not purchase or otherwise acquire any shares
of Preferred Stock other than pursuant to this Section 4 and Section 6.2;
provided, however, that the foregoing shall not prevent the purchase or
acquisition of shares of Preferred Stock pursuant to a purchase or exchange
offer made on the same terms to holders of all outstanding shares of Preferred
Stock.

         SECTION 5. LIQUIDATION. In the event of any complete liquidation,
dissolution or winding- up of the Company, whether voluntary or involuntary, the
holders of shares of Preferred Stock shall each be entitled to receive out of
the assets of the Company legally available for distribution to its stockholders
before any distribution shall be made to the holders of Junior Stock of the
Company,



                                       -8-
<PAGE>   9

for each share of Preferred Stock an amount equal to the greater of (a) the
Deemed Arrearage Value of such share plus $100.00 or (b) the Fair Market Price
of the number of shares of Common Stock into which such share of Preferred Stock
is then convertible pursuant to Section 6 hereof. If, upon any liquidation,
dissolution or winding up of the Company, the assets of the Company, or the
proceeds thereof, shall be insufficient to pay in full the preferential amounts
as to which the Preferred Stock and any other series of Parity Stock would be
entitled, then such assets or the proceeds thereof shall be distributed among
holders of Preferred Stock and the holders of any Parity Stock ratably in
accordance with the respective amounts that would be payable on such shares if
all amounts payable thereon were paid in full.

         SECTION 6. CONVERSION.

         6.1      (a) RIGHT OF HOLDER TO CONVERT. Each share of Preferred Stock
shall be convertible at the option of the record holder thereof at any time
prior to the close of business on the date prior to the redemption date for such
share, into the number of shares of fully paid and nonassessable shares of
Common Stock determined by dividing the sum of $100.00 plus the Deemed Arrearage
Value by the Conversion Price in effect at the time of conversion.

                  (b) MECHANICS OF CONVERSION BY HOLDERS OF PREFERRED STOCK. In
order for any holder of the Preferred Stock to convert the same into Common
Stock, such holder shall present in person or by registered mail, return receipt
requested with postage prepaid thereon, at the principal office of the Company,
the certificate representing such share to the Company by the close of business
on the date prior to the redemption date accompanied by written notice to the
Company that such holder elects to convert all or a specified number of shares
and stating therein its name or the name or names of its nominees in which such
holder wishes the certificate or certificates for Common Stock to be issued. The
Company shall, as soon as practicable thereafter, issue and deliver to such
holder of the Preferred Stock, or to its nominee or nominees, a certificate or
certificates representing the number of shares of Common Stock to which such
holder shall be entitled as aforesaid and, if less than the full number of
shares of the Preferred Stock evidenced by such surrendered certificate or
certificates are being converted, a new certificate or certificates, of like
tenor, for the number of shares of the Preferred Stock evidenced by such
surrendered certificate less the number of such shares being converted.

         6.2      (a) RIGHT OF COMPANY TO CONVERT. Contemporaneous with the
closing of a Qualifying Public Offering, each share of Preferred Stock shall be
automatically converted into the number of fully paid and nonassessable shares
of Common Stock determined by dividing the sum of $100.00 plus the Deemed
Arrearage Value by the Conversion Price in effect at the time of conversion.

                  (b) MECHANICS OF CONVERSION BY THE COMPANY.

                  (i) In the event of a conversion in accordance with this
Section 6.2, the Company shall give notice of such conversion by first class
mail, postage prepaid, mailed not less than 5 nor



                                       -9-
<PAGE>   10

more than 60 days prior to the anticipated closing date of the Qualifying Public
Offering to each holder of record of the shares to be converted, at such
holder's address as the same appears on the stock register of the Company. Each
such notice shall state: (A) the anticipated closing date of the Qualifying
Public Offering; (B) the number of shares of Preferred Stock to be converted;
(C) the Conversion Price as in effect on the conversion date; (D) the number of
shares of Common Stock to be issued upon conversion of each share of Preferred
Stock; (E) the place or places where certificates for such shares are to be
surrendered; and (F) that dividends on the shares to be converted will cease to
accrue on such conversion date. Upon the conversion date, the holders shall
surrender to the Company at the office of the Company the certificate or
certificates representing the Preferred Stock to be converted. The Company
shall, as soon as practicable thereafter, issue and deliver to such holders of
the Preferred Stock, or to their nominee or nominees, certificates representing
the number of shares of Common Stock to which they shall be entitled as
aforesaid.

                  (ii) Notice having been mailed as aforesaid, from and after
the closing date of the Qualifying Public Offering (unless default shall be made
by the Company in issuing shares of Common Stock upon conversion of the
Preferred Stock) dividends on the shares of Preferred Stock so converted shall
cease to accrue, said shares shall no longer be deemed to be outstanding, and
all rights of the holders as holders of shares of Preferred Stock (except the
right to receive from the Company the number of shares of Common Stock issuable
pursuant to this Section 6.2) shall cease. Upon surrender in accordance with
said notice of the certificates for any shares of Preferred Stock to be
converted, shares of Common Stock shall be issued by the Company to the holders
of Preferred Stock. Until so surrendered, certificates for shares of Preferred
Stock shall represent, after the conversion date, the number of shares of Common
Stock into which shares of Preferred Stock have been converted. Share
certificates representing shares of Preferred Stock that are so surrendered
shall be canceled.

         6.3 ADJUSTMENTS TO CONVERSION PRICE FOR DILUTING ISSUES.

                  (a) STOCK DIVIDENDS, SUBDIVISIONS AND COMBINATIONS. In case at
any time or from time to time the Company shall (i) subdivide its outstanding
shares of Common Stock into a larger number of shares of Common Stock or (ii)
combine its outstanding shares of Common Stock into a smaller number of shares
of Common Stock, then the Conversion Price in effect immediately after the
happening of any such event shall be proportionately decreased, in case of the
happening of events described in subparagraph (i) above, or proportionately
increased, in case of the happening of events described in subparagraph (ii)
above.

                  (b) ISSUANCE OF ADDITIONAL SHARES OF COMMON STOCK. In case at
any time or from time to time after the Closing Date, the Company shall (except
as hereinafter provided) issue, whether in connection with the merger of a
corporation into the Company or otherwise, any Additional Shares of Common Stock
for a consideration per share less than the Floor Price on the Computation Date,
then the Conversion Price shall be adjusted to that number determined by
multiplying the Conversion Price in effect immediately prior to such adjustment
by a fraction (x) the numerator of which shall be the number of shares of Common
Stock outstanding on the date of such



                                      -10-
<PAGE>   11

issuance or sale, plus the number of shares of Common Stock which the aggregate
consideration for the total number of such Additional Shares of Common Stock so
issued would purchase at the Floor Price and (y) the denominator of which shall
be the number of shares of Common Stock outstanding on the date of such issuance
or sale plus the number of such Additional Shares of Common Stock so issued.

         No adjustment of the Conversion Price shall be made under this Section
6.3(b) upon the issuance of any Additional Shares of Common Stock which are
issued pursuant to the exercise of any warrants or other subscription or
purchase rights or pursuant to the exercise of any conversion or exchange rights
in any Convertible Securities, if any such adjustment shall previously have been
made upon the issuance of such warrants or other rights or upon the issuance of
such Convertible Securities (or upon the issuance of any warrant or other rights
therefor) pursuant to Section 6.3(c) or 6.3(d).

                  (c) ISSUANCE OF WARRANTS, OPTIONS OR OTHER RIGHTS. In case at
any time or from time to time after the Closing Date, the Company shall issue
(other than as a dividend or distribution to holders of its Common Stock), any
warrants, options or other rights to subscribe for or purchase any Additional
Shares of Common Stock or any Convertible Securities and the consideration per
share for which Additional Shares of Common Stock may at any time thereafter be
issuable pursuant to such warrants, options or other rights or pursuant to the
terms of such Convertible Securities shall be less than the Floor Price on the
Computation Date then the Conversion Price shall be adjusted as provided in
Section 6.3(b). Such adjustment shall be made on the basis that (i) the maximum
number of Additional Shares of Common Stock issuable pursuant to all such
warrants, options or other rights or necessary to effect the conversion or
exchange of all such Convertible Securities shall be deemed to have been issued
as of the Computation Date, and (ii) the aggregate consideration for such
maximum number of Additional Shares of Common Stock shall be deemed to be the
minimum consideration received and receivable by the Company for the issuance of
such Additional Shares of Common Stock pursuant to such warrants, options or
other rights or pursuant to the terms of such Convertible Securities.

                  (d) ISSUANCE OF CONVERTIBLE SECURITIES. In case at any time or
from time to time after the Closing Date, the Company shall issue (other than as
a dividend or distribution to holders of its Common Stock) any Convertible
Securities and the consideration per share for which Additional Shares of Common
Stock may at any time thereafter be issuable pursuant to the terms of such
Convertible Securities shall be less than the Floor Price on the Computation
Date, then the Conversion Price shall be adjusted as provided in Section 6.3(b).
Such adjustments shall be made on the basis that (i) the maximum number of
Additional Shares of Common Stock necessary to effect the conversion or exchange
of all such Convertible Securities shall be deemed to have been issued as of the
Computation Date, and (ii) the aggregate consideration for such maximum number
of Additional Shares of Common Stock shall be deemed to be the minimum
consideration received and receivable by the Company for the issuance of such
Additional Shares of Common Stock pursuant to the terms of such Convertible
Securities. No adjustment of the Conversion Price shall be made under this
Section 6.3(d) upon the issuance of any Convertible Securities which are issued



                                      -11-
<PAGE>   12

pursuant to the exercise of any warrants or other subscription or purchase
rights therefor, if any such adjustment shall previously have been made upon the
issuance of such warrants or other rights pursuant to Section 6.3(c).

                  (e) SUPERSEDING ADJUSTMENT OF CONVERSION PRICE. If, at any
time after any adjustment of the Conversion Price shall have been made pursuant
to the foregoing Section 6.3(c) or 6.3(d) on the basis of the issuance of
warrants or other rights or the issuance of other Convertible Securities, or
after any new adjustment of the Conversion Price shall have been made pursuant
to this 6.3(e):

                  (i) all of such warrants, options or rights or the right of
conversion or exchange in such other Convertible Securities shall expire, and
not all of such warrants, options or rights, or the right of conversion or
exchange in respect of such other Convertible Securities, as the case may be,
shall have been exercised; or

                  (ii) the consideration per share, for which Additional Shares
of Common Stock are issuable pursuant to all of such warrants, options or rights
or the terms of all of such other Convertible Securities, shall be increased
solely by virtue of provisions therein contained for an automatic increase in
such consideration per share upon the arrival of a specified date or the
happening of a specified event, and none of such warrants, options or rights, or
the right of conversion or exchange in respect of such other Convertible
Securities, as the case may be, shall have been exercised;

then such previous adjustment shall be rescinded and annulled and the Additional
Shares of Common Stock which were deemed to have been issued by virtue of the
computation made in connection with the adjustment so rescinded and annulled
shall no longer be deemed to have been issued by virtue of such computation.
Thereupon, a recomputation shall be made of the effect of such warrants, rights
or options or other Convertible Securities on the basis of treating any such
warrants, options or rights or any such other Convertible Securities which then
remain outstanding as having been granted or issued immediately after the time
of such increase of the consideration per share for such Additional Shares of
Common Stock are issuable under such warrants or rights or other Convertible
Securities; and, if and to the extent called for by the foregoing provisions of
this Section 6.3 on the basis aforesaid, a new adjustment of the Conversion
Price shall be made, which new adjustment shall supersede the previous
adjustment so rescinded and annulled.

                  (f) OTHER PROVISIONS APPLICABLE TO ADJUSTMENTS UNDER THIS
SECTION. The following provisions shall be applicable to the making of
adjustments of the Conversion Price hereinbefore provided for in this Section
6.3:

                  (i) Treasury Stock. The sale or other disposition of any
issued shares of Common Stock owned or held by or for the account of the Company
shall be deemed an issuance thereof for purposes of this Section 6.3.



                                      -12-
<PAGE>   13

                  (ii) Computation of Consideration. To the extent that any
Additional Shares of Common Stock or any Convertible Securities or any warrants,
options or other rights to subscribe for or purchase any Additional Shares of
Common Stock or any Convertible Securities shall be issued solely for cash
consideration, the consideration received by the Company therefor shall be
deemed to be the amount of cash received by the Company therefor, or, if such
Additional Shares of Common Stock or Convertible Securities are offered by the
Company for subscription, the subscription price, or, if such Additional Shares
of Common Stock or Convertible Securities are sold to underwriters or dealers
for public offering without a subscription offering, the initial public offering
price, in any such case excluding any amounts paid or receivable for accrued
interest or accrued dividends and without deduction of any compensation,
discounts or expenses paid or incurred by the Company for and in the
underwriting of, or otherwise in connection with, the issue thereof. The
consideration for any Additional Shares of Common Stock issuable pursuant to any
warrants, options or other rights to subscribe for or purchase the same shall be
the consideration received or receivable by the Company for issuing such
warrant, options or other rights, plus the additional consideration payable to
the Company upon the exercise of such warrants, options or other rights. The
consideration for any Additional Shares of Common Stock issuable pursuant to the
terms of any Convertible Securities shall be the consideration received or
receivable by the Company for issuing any warrants or other rights to subscribe
for or purchase such Convertible Securities, plus the consideration paid or
payable to the Company in respect of the subscription for or purchase of such
Convertible Securities, plus the additional consideration, if any, payable to
the Company upon the exercise of the right of conversion or exchange in such
Convertible Securities. To the extent that any issuance shall be for a
consideration other than solely for cash, then, except as herein otherwise
expressly provided, the amount of such consideration shall be deemed to be the
fair value of such consideration at the time of such issuance as determined
pursuant to the Valuation Procedure.

                  (iii) When Adjustments to be made. The adjustments required by
the preceding subsections of this Section 6.3 shall be made whenever and as
often as any specified event requiring an adjustment shall occur, except that no
adjustment of the Conversion Price that would otherwise be required shall be
made (except in the case of a subdivision or combination of shares of the Common
Stock as provided for in Section 6.3(a)) unless and until such adjustment,
either by itself or with other adjustments not previously made, adds or
subtracts at least $0.05 to the Conversion Price, as determined in good faith by
the Board of Directors of the Company. Any adjustment representing a change of
less than such minimum amount shall be carried forward and made as soon as such
adjustment, together with other adjustments required by this Section 6.3 and not
previously made, would result in a minimum adjustment. 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.

                  (iv) Fractional Interests. In computing adjustments under this
Section 6.3, fractional interests in Common Stock shall be taken into account to
the nearest one-thousandth of a share.

                  (g) MERGER, CONSOLIDATION OR DISPOSITION OF ASSETS. In case
the Company shall merge or consolidate into another corporation, or shall sell,
transfer or otherwise dispose of all or



                                      -13-
<PAGE>   14

substantially all of its property, assets or business to another corporation,
then each holder of a share of the Preferred Stock shall have the right
thereafter to convert such shares only into the kind and amount of shares of
stock and other securities and property receivable upon or deemed to be held
following such merger, consolidation, sale, transfer or disposition of assets by
a holder of a number of shares of the Common Stock of the Company into which
such shares of Preferred Stock could have been converted immediately prior to
such merger, consolidation, sale, transfer or disposition of assets. In case of
any such merger, consolidation, sale, transfer or disposition of assets, the
successor acquiring corporation shall expressly assume the due and punctual
observance and performance of each and every covenant and condition hereof to be
performed and observed by the Company and all of the obligations and liabilities
hereunder, subject to such modification as shall be necessary to provide for
adjustments to the Conversion Price which shall be as nearly equivalent as
practicable to the adjustments provided for in this Section 6.3. The foregoing
provisions of this Section 6.3(g) shall similarly apply to successive mergers,
consolidations or dispositions of assets.

                  (h) OTHER ACTION AFFECTING COMMON STOCK. In case at any time
or from time to time the Company shall take any action affecting its Common
Stock, other than an action described in any of the foregoing Sections 6.3(a)
through 6.3(g), inclusive, then, unless in the opinion of the Board of Directors
such action will not have a materially adverse effect upon the rights of the
holders of the Preferred Stock, the Conversion Price shall be adjusted in such
manner and at such time as the Board of Directors may in good faith determine to
be equitable in the circumstances.

         6.4 NO IMPAIRMENT. The Company will at all times in good faith assist
in the carrying out of all the provisions of this Section 6 and in the taking of
all such action as may be necessary or appropriate in order to protect the
conversion rights of the holders of the Preferred Stock against impairment.
Without limiting the generality of the foregoing, the Company (i) will not
permit the par value of any shares of stock at the time receivable upon the
conversion of the Preferred Stock to exceed the Conversion Price then in effect,
(ii) will take all such action as may be necessary or appropriate in order that
the Company may validly and legally issue fully paid nonassessable shares of
stock on the conversion of the Preferred Stock and (iii) will not issue any
Common Stock or Convertible Securities or take any action which results in any
adjustment of the Conversion Price if the total number of shares of Common Stock
issuable after such issuance or action upon the conversion or redemption of, or
payment of all outstanding dividends on, all of the then outstanding shares of
Preferred Stock will exceed the total number of shares of Common Stock then
authorized by the Company's Certificate of Incorporation and available for the
purpose of issue upon such conversion or redemption or payment of such dividend.

         6.5 CERTIFICATE AS TO ADJUSTMENTS. Upon the occurrence of each
adjustment or readjustment of the Conversion Price pursuant to Section 6.3, the
Company at its expense shall promptly compute such adjustment or readjustment in
accordance with the terms hereof and furnish to each holder of the Preferred
Stock a certificate setting forth such adjustment or readjustment and showing in
detail the facts upon which such adjustment or readjustment is based, including
a statement of (i) the consideration received or to be received by the Company
for any Common Stock issued or sold or deemed to have been issued, (ii) the
number of shares of Common Stock



                                      -14-
<PAGE>   15

outstanding or deemed to be outstanding and (iii) the Conversion Price in effect
immediately prior to such issue or sale and as adjusted and readjusted on
account thereof, showing how it was calculated. The Company shall, upon the
written request at any time of any holder of the Preferred Stock, furnish or
cause to be furnished to such holder a like certificate setting forth (i) the
Conversion Price at the time in effect, showing how it was calculated, and (ii)
the number of shares of Common Stock and the amount, if any, of other property
which at the time would be received upon the conversion of the Preferred Stock.

         6.6 NOTICES OF RECORD DATE. In the event of any taking by the Company
of a record of the holders of any class of securities for the purpose of
determining the holders thereof who are entitled to receive any dividend or
other distribution, or any right to subscribe for, purchase or otherwise acquire
any shares of stock of any class or any other securities or property, or to
receive any other right, the Company shall use commercially reasonable efforts
to mail to each holder of the Preferred Stock at least ten days prior to the
date specified therein, a notice specifying the date on which any such record is
to be taken for the purpose of such dividend or distribution.

         6.7 RESERVATION OF SHARES. The Company covenants that it will at all
times reserve and keep available, out of its authorized and unissued Common
Stock solely for the purpose of issuance upon conversion of Preferred Stock as
herein provided, free from preemptive rights or any other actual or contingent
purchase rights of persons other than the holders of shares of Preferred Stock,
such number of shares of Common Stock as shall then be issuable upon the
conversion of all outstanding shares of Preferred Stock. The Company covenants
that all shares of Common Stock that shall be so issuable shall upon issue be
duly and validly issued and fully paid and nonassessable.

         SECTION 7. VOTING RIGHTS OF PREFERRED STOCK.

         7.1 GENERAL VOTING RIGHTS. Holders of Preferred Stock shall be
entitled, on all matters submitted for a vote of the holders of Common Stock,
whether pursuant to law or otherwise, to vote together as one class with the
holders of Common Stock and the holders of all other shares of stock entitled to
vote with the holders of Common Stock on such matters. The holders of the
Preferred Stock shall be entitled to a number of votes per share of the
Preferred Stock equal to the number of shares of Common Stock issuable upon
conversion of one share of Preferred Stock on the date of such vote.

         7.2 VOTE OF SERIES REQUIRED. So long as any shares of Preferred Stock
are outstanding, the affirmative vote of the holders of a majority of the shares
of Preferred Stock outstanding at the time shall be necessary to permit, effect
or validate

                  (a) the authorization, creation or issuance, or any increase
in the authorized or issued amount, of any class or series of Senior Stock or
Parity Stock; and

                  (b) the amendment, alteration or repeal of any of the
provisions of the Restated Certificate of Incorporation which would adversely
affect the voting powers, designations,



                                      -15-
<PAGE>   16
preferences, redemption rights, and relative participating, optional or other
rights and the qualifications, limitations or restrictions of the Preferred
Stock.

         7.3 CONFLICTS. To the extent permitted by applicable law, in the event
of any conflict or inconsistency between (i) any of the provisions of this
Section 7 or any other provision in this Certificate and (ii) the Certificate of
Incorporation or the Bylaws of the Company, as may be amended from time to time,
the terms of this Certificate shall supersede such conflicting or inconsistent
provision and shall control.

         IN WITNESS WHEREOF, ENERGY PARTNERS, LTD. has caused its corporate seal
to be hereunto affixed and this certificate to be executed this 16th day of
November, 1999.

                                       ENERGY PARTNERS, LTD.



                                       By:
                                          --------------------------------------



                                      -16-