<PAGE>

                                                                     EXHIBIT 3.4

                          CERTIFICATE OF DESIGNATIONS
                                      OF
                SERIES C CUMULATIVE CONVERTIBLE PREFERRED STOCK
                                      OF
                             THE WISER OIL COMPANY

                        Pursuant to Section 151 of the
                       Delaware General Corporation Law


     The Wiser Oil Company, a Delaware corporation (the "Corporation"), does
hereby certify in accordance with Section 103 of the Delaware General
Corporation Law (the "DGCL") that the following resolution was duly adopted by
action of the Board of Directors of the Corporation (the "Board"):

     RESOLVED, that pursuant to the authority expressly granted to and vested in
the Board by the provisions of Article Fourth of the Restated Certificate of
Incorporation of the Corporation (the "Certificate of Incorporation"), and
pursuant to Section 151 of the DGCL, the Board hereby creates a series of
preferred stock of the Corporation and hereby states that the voting powers,
designations, preferences and relative, participating, optional or other special
rights of which, and qualifications, limitations or restrictions thereof (in
addition to the provisions set forth in the Certificate of Incorporation which
are applicable to the preferred stock of all classes and series), shall be as
follows:

     Section 1.     Number of Shares and Designation.
                    --------------------------------

     This series of preferred stock shall be designated as the Series C
Cumulative Convertible Preferred Stock (the "Series C Preferred"), and the
number of shares that shall constitute such series shall be 1,000,000 shares,
par value $10.00 per share (the "Shares"), which number may be decreased (but
not below the number thereof then outstanding) from time to time by the Board.

     Section 2.     Dividends.
                    ---------

     2A.  General Obligation.  When, as and if declared by the Board and to the
          ------------------
extent permitted under the DGCL, the Corporation shall pay preferential
dividends in cash or Common Stock (as defined in Section 11 hereof) to the
holders of the Series C Preferred as provided in this Section 2.  Dividends on
each Share of the Series C Preferred shall accrue on a daily basis at the rate
of seven percent (7%) per annum of the Liquidation Value (as defined in Section
11 hereof) of such Share from and including the date of issuance of such Share
to and including the first to occur of (i) the date on which the Liquidation
Value of such Share (plus all accrued and unpaid dividends thereon) is due and
payable to the holder thereof in connection with the Liquidation (as defined in
Section 3 hereof) of the Corporation, (ii) the date on which such Share is
converted into shares of Common Stock hereunder or (iii) the date on which such
Share is otherwise acquired by the Corporation.  Such dividends shall accrue
whether or not they have been declared and whether or not there are profits,
surplus or other funds of the Corporation legally available for the payment of
dividends.
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     2B.  Dividend Payment Dates.  All dividends that have accrued on the Series
          ----------------------
C Preferred shall be payable on March 31, June 30, September 30 and December 31
of each year, beginning on the first such date immediately following the Closing
Date (as defined in Section 11 hereof) (the "Dividend Payment Dates").  All
dividends that have accrued on each Share outstanding during the three-month
period (or other period in the case of an initial Dividend Payment Date) ending
upon such Dividend Payment Date shall be accumulated and shall remain
accumulated dividends with respect to such Share until paid to the holder
thereof; provided, however, that accumulations of dividends accrued on the
Series C Preferred shall not bear interest.  If a Dividend Payment Date falls on
any date other than a Business Day (as defined in Section 11 hereof), the
dividend payment due on such Dividend Payment Date shall be paid on the Business
Day immediately following such Dividend Payment Date, with the same effect as if
paid on the Dividend Payment Date without any additional accrual of dividends
payable in respect of such delay.  Dividends payable on each Dividend Payment
Date shall be paid to record holders of the Shares as they appear on the books
of the Corporation at the close of business on a date fixed by the Board not
more than 60 days immediately preceding the applicable Dividend Payment Date.
Cumulative and unpaid dividends on Series C Preferred for any past quarterly
dividend periods may be paid at any time, without reference to any regular
Dividend Payment Date, to holders of record of such Shares on such date, not
exceeding 60 days immediately preceding the payment date thereof, as may be
fixed by the Board.

     2C.  Distribution of Partial Dividend Payments.  Except as otherwise
          -----------------------------------------
provided herein, if at any time the Corporation pays less than the total amount
of dividends then accrued with respect to the Series C Preferred, such payment
shall be distributed pro rata among the holders thereof based upon the aggregate
accrued but unpaid dividends on the Shares held by each such holder.

     2D.  Payment of Dividends  in Common Stock.  The Corporation shall have the
          -------------------------------------
option of paying dividends accruing on the Series C Preferred either in cash, by
the issuance or delivery of shares of Common Stock ("PIK Dividends") or any
combination thereof.  If the Corporation elects to pay any dividends accruing on
the Series C Preferred not in cash but as PIK Dividends, the number of shares of
Common Stock to be issued or delivered in payment of such dividends shall be
determined by dividing the amount of cash that would otherwise be paid by the
average Market Price (as defined in Section 11 hereof) of the Common Stock for
the 10 trading days immediately preceding (but not including) the date of
payment of such PIK Dividend.  If the Corporation pays PIK Dividends, such
payment in shares of Common Stock shall be made pro rata among the holders of
the Series C Preferred based upon the aggregate accrued but unpaid dividends on
the Shares held by each such holder, with cash paid in lieu of the issuance of
fractional shares of Common Stock to the extent permitted under the
Corporation's Loan Agreements (as defined in Section 11 hereof); any amounts not
payable in lieu of fractional shares due to restrictions in the Loan Agreements
shall continue to be payable as accrued and unpaid dividends.  All shares of
Common Stock when issued or delivered as PIK Dividends under this Section 2D
shall be duly and validly issued, fully paid and nonassessable and shall be free
from all taxes (other than income taxes payable by the holder) with respect to
the issue thereof and all liens, charges and encumbrances created by, through or
under the Corporation.  The Corporation shall at all times reserve and keep
available out of its authorized but unissued shares of Common Stock, solely for
the purpose of the issuance of PIK Dividends, a number of shares of Common Stock
it reasonably determines will be required to be issued as PIK Dividends.  The
Corporation shall take all such actions as may be reasonably necessary to assure
that

                                      -2-
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all shares of Common Stock to be issued or delivered as PIK Dividends may be
issued or delivered without violation of any applicable law or governmental
regulation and shall use commercially reasonable efforts to satisfy any
requirements of any domestic securities exchange upon which shares of Common
Stock may be listed with respect to the issuance or delivery of PIK Dividends
(except for official notice of issuance, which shall be immediately delivered by
the Corporation upon each such issuance).

     Section 3.     Liquidation.
                    -----------

     Upon any liquidation, dissolution or winding up of the Corporation, whether
voluntary or involuntary (a "Liquidation"), each holder of Series C Preferred
shall be entitled to receive, out of the assets of the Corporation available for
distribution to stockholders, before any distribution or payment is made upon
any Junior Securities (as defined in Section 11 hereof), an amount in cash equal
to the aggregate Liquidation Value of all Shares held by such holder plus all
accrued and unpaid dividends thereon through the effective date of the
Liquidation.  After payment to the holders of the Series C Preferred in full of
the preferential amounts provided for in this Section 3, the holders of Series C
Preferred shall have no right or claim to any of the remaining assets of the
Corporation. If upon any Liquidation the Corporation's assets to be distributed
among the holders of the Series C Preferred are insufficient to permit payment
to such holders of the aggregate amount which they are entitled to be paid under
this Section 3, then the entire assets available to be distributed to the
Corporation's stockholders shall be distributed pro rata among such holders
based upon the aggregate Liquidation Value (plus all accrued and unpaid
dividends thereon through the effective date of the Liquidation) of the Series C
Preferred held by each such holder.  Not less than 30 days prior to the payment
date stated therein, the Corporation shall mail written notice of any such
Liquidation to each record holder of Series C Preferred as of a date at least
three Business Days prior to the mailing of such notice, setting forth in
reasonable detail the amount of proceeds to be paid with respect to each Share
of the Series C Preferred and each share of Common Stock in connection with such
Liquidation (assuming no conversion of Shares into Common Stock).  At any time
prior to a Liquidation, the holders of the Series C Preferred shall be entitled
to convert their Shares into Common Stock in accordance with the provisions of
Section 6 hereof.  Neither the consolidation or merger of the Corporation into
or with any other entity or entities (whether or not the Corporation is the
surviving entity), nor the sale, conveyance, exchange or transfer (for cash,
securities or other consideration) by the Corporation of all or any part of its
assets, nor the reduction of the capital stock of the Corporation nor any other
form of recapitalization or reorganization affecting the Corporation shall be
deemed to be a Liquidation within the meaning of this Section 3.

     Section 4.     Priority of Series C Preferred on Dividends and Redemptions.
                    -----------------------------------------------------------

     So long as any Series C Preferred remains outstanding, without the prior
written consent of the holders of at least two-thirds of the outstanding Shares,
and except for any repurchases of Common Stock in odd-lot tender offers, the
Corporation shall not, nor shall it permit any Subsidiary (as defined in Section
11 hereof) to, redeem, purchase or otherwise acquire directly or indirectly for
value any Junior Securities, nor shall the Corporation declare or pay any
dividend or make any distribution upon any Junior Securities, if at the time of
or immediately after any such redemption, purchase, acquisition, dividend or
distribution the Corporation has failed to pay the full amount of dividends
accrued on the Series C Preferred for all quarterly dividend periods terminating
on or prior

                                      -3-
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to the date on which such redemption, purchase, acquisition, dividend or
distribution is to occur; provided that the foregoing shall not prohibit the
purchase or other acquisition of Junior Securities or rights to acquire Junior
Securities from directors, officers or employees of the Corporation or its
Subsidiaries in connection with the termination of their directorships or
employment.

     Section 5.     Voting Rights.
                    -------------

     5A.  Voting Procedures.  The holders of the Series C Preferred shall be
          -----------------
entitled to notice of all meetings of the Corporation's stockholders in
accordance with the Corporation's bylaws and applicable law.  Each Share of
Series C Preferred shall have one (1) vote per Share, except that when the
holders of the Series C Preferred and the Common Stock shall vote together as a
single class, then each holder of Series C Preferred shall be entitled to the
number of votes with respect to such holder's Shares of Series C Preferred equal
to the number of whole shares of Conversion Stock (as defined in Section 11
hereof) into which such Shares would have been converted under the provisions of
Section 6A hereof (whether or not such holder is then entitled to convert such
Shares under such Section) at the Conversion Price (as defined in Section 11
hereof) in effect on the record date for determining stockholders entitled to
vote on such matters or, if no record date is specified, as of the date of such
vote.

     5B.  General Voting Rights.  The holders of the Series C Preferred shall
          ---------------------
vote together as a single class with the holders of the Common Stock as provided
in Section 5A hereof on all matters submitted to a vote of the holders of the
Common Stock.  Except as otherwise expressly provided herein or by applicable
law, the holders of the Shares of Series C Preferred shall not be entitled to
vote as a separate class on any matters submitted to a vote of the stockholders.

     5C.  Special Voting Rights.  In addition to the voting rights provided in
          ---------------------
Section 5B hereof and any voting rights provided by applicable law, so long as
any Series C Preferred remains outstanding, (i) the holders of at least two-
thirds of the Series C Preferred outstanding must approve, voting separately as
a class, any amendment to the Certificate of Incorporation that would alter or
change the powers, preferences or special rights of the Shares of Series C
Preferred so as to affect them adversely and (ii) the holders of a majority of
the Series C Preferred outstanding must approve, voting separately as a class,
any proposed issuance of capital stock of the Corporation that ranks pari passu
with or senior to the Series C Preferred as to dividends or assets, or any
proposed issuance of capital stock of the Corporation that is required to be
redeemed by the Corporation at any time that any Shares of Series C Preferred
are outstanding, whether upon the occurrence of certain events or otherwise.

     Section 6.     Conversion.
                    ----------

     6A.  Conversion at Option of Holder.
          ------------------------------

          (i)    At any time and from time to time after the 90th day following
the Closing Date, any holder of Series C Preferred may convert all or any
portion of the Series C Preferred held by such holder into a number of shares of
Common Stock computed by dividing (x) the total amount of Liquidation Value
(plus the aggregate accrued but unpaid dividends, if any) represented by the
Shares to be converted by (y) the Conversion Price then in effect.

                                      -4-
<PAGE>

          (ii)   Each conversion of Series C Preferred pursuant to this Section
6A shall be deemed to have been effected as of the close of business on the date
on which the certificate or certificates representing the Series C Preferred to
be converted (duly endorsed or assigned to the Corporation or in blank) have
been surrendered for conversion during normal business hours at the principal
office of the Corporation, accompanied by written notice to the Corporation that
the holder thereof elects to convert all or any portion of such Shares.
Notwithstanding the immediately preceding sentence, if a conversion of Series C
Preferred pursuant to this Section 6A is to be made in connection with or in
anticipation of a material transaction affecting the Corporation, such
conversion may, at the election of the holder thereof, be conditioned upon the
consummation of such transaction, in which case such conversion (a) shall not be
deemed to be effective until immediately prior to the consummation of such
transaction and (b) shall be made based upon the Conversion Price in effect
immediately prior to the consummation of such transaction.

     6B.  Mandatory Conversions.
          ---------------------

          (i)    If, at any time from and after the Closing Date, the Market
Price of the Common Stock exceeds $10.00 per share (which amount shall be
proportionately adjusted for any recapitalization, stock split, reverse stock
split, stock dividend or similar event resulting in a change in the shares of
Common Stock) on each of 60 consecutive trading days, then all Shares of the
Series C Preferred then outstanding shall automatically be deemed to have been
surrendered by the holders thereof for conversion (and shall be automatically
converted) into shares of Common Stock as provided in the next following
sentence effective as of the close of business on the last day of such 60-day
period. Each holder's Shares of Series C Preferred shall be converted into a
number of shares of Common Stock computed by dividing (x) the total amount of
Liquidation Value (plus the aggregate accrued but unpaid dividends, if any)
represented by such holder's Shares by (y) the Conversion Price in effect as of
the close of business on the last day of such 60-day period.

          (ii)   The Corporation shall have the right, at its sole option, to
convert all, but not less than all, of the then outstanding Shares of Series C
Preferred into shares of Common Stock as provided in the next following sentence
effective as of the close of business on the Business Day immediately preceding
the date of consummation of any Corporate Change (as defined in Section 6G
hereof); provided, however, that such conversion shall be subject to and
conditioned upon the consummation of such Corporate Change.  If the Corporation
elects to exercise this special conversion right and the Corporate Change is
consummated, each holder's Shares of Series C Preferred shall automatically be
deemed to have been surrendered by such holder for conversion (and shall be
automatically converted) into a number of shares of Common Stock computed by
dividing (x) the total amount of Liquidation Value (plus the aggregate accrued
but unpaid dividends, if any) represented by such holder's Shares by (y) the
Conversion Price in effect as of the close of business on the Business Day
immediately preceding the date of consummation of such Corporate Change. The
Corporation  may exercise this special conversion right by mailing to the
holders of record of the Series C Preferred at least 20 days in advance of the
expected effective date of the Corporate Change a written notice of its election
to do so, which notice shall include (a) a summary description of the Corporate
Change, (b) a statement that the Corporation elects to exercise its special
conversion right under this Section 6B(ii) in connection with such Corporate
Change and (c) the expected effective date of such Corporate Change.  The
exercise by the Corporation of this special conversion right shall be
irrevocable.

                                      -5-
<PAGE>

          (iii)  All Shares of the Series C Preferred that remain outstanding
at the close of business on the Mandatory Conversion Date (as defined in Section
11 hereof) shall automatically be deemed to have been surrendered by the holders
thereof for conversion (and shall be automatically converted) into shares of
Common Stock as provided in the next following sentence effective as of the
close of business on the Mandatory Conversion Date.  Each holder's Shares of
Series C Preferred shall be converted into a number of shares of Common Stock
computed by dividing (x) the total amount of Liquidation Value (plus the
aggregate accrued but unpaid dividends, if any) represented by such holder's
Shares by (y) the Conversion Price in effect as of the close of business on the
Mandatory Conversion Date.

     6C.  Conversion Procedures.
          ---------------------

          (i)    At the time any conversion of Series C Preferred pursuant to
this Section 6 has been effected, the rights of the holder of the Shares
converted as a holder of Series C Preferred shall cease, and the person or
persons in whose name or names any certificate or certificates for shares of
Conversion Stock are to be issued upon such conversion shall be deemed to have
become the holder or holders of record of the shares of Conversion Stock
represented thereby.

          (ii)   As soon as practicable after a conversion of Series C Preferred
pursuant to this Section 6 has been effected (but in any event within five
Business Days thereafter), the Corporation shall deliver or cause to be
delivered to the record holder of the Shares converted:

                 (a) unless in book-entry form, a certificate or certificates
     representing the number of shares of Conversion Stock issuable by reason of
     such conversion in such name or names and such denomination or
     denominations as such holder has specified;

                 (b) payment in cash of the amount, if any, payable under
     subparagraph (vi) below with respect to fractional shares upon such
     conversion; and

                 (c) a certificate representing any Shares of Series C Preferred
     that were represented by the certificate or certificates delivered to the
     Corporation in connection with such conversion but which were not
     converted;

provided, however, that in the event of a conversion of the Series C Preferred
pursuant to Section 6B hereof, the items referred to in clauses (a) and (b)
above shall be delivered as soon as practicable (but in any event within five
Business Days) after the certificates representing the Shares are actually
surrendered for conversion during normal business hours at the principal office
of the Corporation.

          (iii)  The issuance or delivery of certificates for shares of
Conversion Stock upon conversion of Series C Preferred shall be made without
charge to the holders of such Series C Preferred for any issuance tax in respect
thereof or other cost incurred by the Corporation in connection with such
conversion and the related issuance of shares of Conversion Stock; provided,
however, that the Corporation shall not be required to pay any tax which may be
payable in respect of any transfer involved in the issuance and delivery of any
such certificate in a name other than that of the record holder of Shares
converted.

                                      -6-
<PAGE>

          (iv)   The Corporation shall not close its books against the transfer
of Series C Preferred or of Conversion Stock issued or issuable upon conversion
of Series C Preferred in any manner that interferes in any material respect with
the timely conversion of Series C Preferred. The Corporation shall assist and
cooperate with any holder of Shares required to make any governmental filings or
obtain any governmental approvals prior to or in connection with any conversion
of Shares hereunder (including, without limitation, making any filings required
to be made by the Corporation).

          (v)    The Corporation shall at all times reserve and keep available
out of its authorized but unissued shares of Common Stock, solely for the
purpose of issuance upon the conversion of the Series C Preferred, such number
of shares of Common Stock issuable upon the conversion of all outstanding Series
C Preferred. All shares of Common Stock which are so issuable shall be free of
preemptive rights and shall, when issued, be duly and validly issued, fully paid
and nonassessable and free from all taxes (other than income taxes payable by
the holder) with respect to the issue thereof and all liens, charges and
encumbrances created by, through or under the Corporation. The Corporation shall
not take any action which would cause the number of authorized but unissued
shares of Common Stock to be less than the number of such shares required to be
reserved hereunder for issuance upon conversion of the Series C Preferred.

          (vi)   If any fractional interest in a share of Conversion Stock
would, except for the provisions of this subparagraph (vi), be delivered upon
any conversion of the Series C Preferred, the Corporation, in lieu of delivering
the fractional share therefor, shall pay an amount to the holder thereof equal
to the Market Price of such fractional interest as of the third Business Day
preceding the date of conversion to the extent permitted under the Corporation's
Loan Agreements.

     6D.  Conversion Price.
          ----------------

          (i)    The initial Conversion Price shall be $4.25. In order to
prevent dilution of the conversion rights granted under this Section 6, the
Conversion Price shall be subject to adjustment from time to time pursuant to
this Section 6D.

          (ii)   If and whenever after the Closing Date, the Corporation issues
or sells for cash, marketable securities or cash equivalents, or in accordance
with Section 6E hereof is deemed to have issued or sold for cash, marketable
securities or cash equivalents, any Common Stock for a consideration per share
less than the average Market Price of the Common Stock for the 30 trading days
immediately preceding (but not including) the date of such issue or sale, then
immediately upon such issue or sale the Conversion Price shall be reduced to the
Conversion Price determined by multiplying the Conversion Price in effect
immediately prior to such issue or sale by a fraction, the numerator of which
shall be the sum of (1) the number of shares of Common Stock Deemed Outstanding
(as defined in Section 11 hereof) immediately prior to such issue or sale plus
(2) the number of shares of Common Stock which the aggregate consideration
received (and deemed to be received hereunder) by the Corporation upon such
issue or sale would purchase at such average Market Price, and the denominator
of which shall be the number of shares of Common Stock Deemed Outstanding
immediately after such issue or sale.

                                      -7-
<PAGE>

          (iii)  Notwithstanding anything contained herein to the contrary, no
adjustment of the Conversion Price pursuant to this Section 6D or Section 6E
hereof shall be made (a) upon the issuance or conversion of Series C Preferred
or the payment of any PIK Dividend, (b) upon the issuance or sale of Common
Stock, Options (as defined in Section 11 hereof) or Convertible Securities (as
defined in Section 11 hereof) to directors, officers and employees of the
Corporation and its Subsidiaries pursuant to the terms of any employee benefit
or similar plans of the Corporation or any of its Subsidiaries, including the
issuance or sale of Common Stock pursuant to any such Options or Convertible
Securities as are outstanding as of the Closing Date, (c) upon the issuance or
sale of Common Stock or Options pursuant to the terms of the Warrant Agreement
(as defined in Section 11 hereof), (d) on account of any change in the terms of
or any expiration or termination of any of the Options or Convertible Securities
referred to in clauses (b) and (c) above or (e) in connection with any of the
events or upon the issuance or sale of any Common Stock, Options or Convertible
Securities referred to in Sections 7 and 8 hereof.

     6E.  Effect on Conversion Price of Certain Events.  For purposes of
          --------------------------------------------
determining the adjusted Conversion Price under Section 6D hereof, the following
shall be applicable:

          (i)    Issuance of Options.  If the Corporation in any manner grants,
                 -------------------
issues or sells any Options and the price per share for which Common Stock is
issuable upon the exercise of such Options, or upon conversion or exchange of
any Convertible Securities issuable upon the exercise of such Options, is less
than the average Market Price of the Common Stock for the 30 trading days
immediately preceding (but not including) the date of such grant, issue or sale
of Options, then the total maximum number of shares of Common Stock issuable
upon the exercise of such Options or upon conversion or exchange of the total
maximum amount of such Convertible Securities issuable upon the exercise of such
Options shall be deemed to be outstanding and to have been issued and sold by
the Corporation at the time of the granting, issue or sale of such Options for
such price per share.  For purposes of this Section 6E(i), the "price per share
for which Common Stock is issuable" shall be determined by dividing (a) the
total amount, if any, received or receivable by the Corporation as consideration
for the granting, issue or sale of such Options, plus the minimum aggregate
amount of additional consideration payable to the Corporation upon exercise of
all such Options, plus in the case of such Options which relate to Convertible
Securities, the minimum aggregate amount of additional consideration, if any,
payable to the Corporation upon the issuance or sale of such Convertible
Securities and the conversion or exchange thereof, by (b) the total maximum
number of shares of Common Stock issuable upon the exercise of such Options or
upon the conversion or exchange of all such Convertible Securities issuable upon
the exercise of such Options.  No further adjustment of the Conversion Price
shall be made when Convertible Securities are actually issued upon the exercise
of such Options or when Common Stock is actually issued upon the exercise of
such Options or the conversion or exchange of such Convertible Securities.

          (ii)   Issuance of Convertible Securities.  If the Corporation in any
                 ----------------------------------
manner issues or sells any Convertible Securities and the price per share for
which Common Stock is issuable upon conversion or exchange thereof is less than
the average Market Price of the Common Stock for the 30 trading days immediately
preceding (but not including) the date of such issue or sale of Convertible
Securities, then the total maximum number of shares of Common Stock issuable
upon conversion or exchange of such Convertible Securities shall be deemed to be
outstanding and to have been issued and sold by the Corporation at the time of
the issuance or sale of such Convertible

                                      -8-
<PAGE>

Securities for such price per share. For purposes of this Section 6E(ii), the
"price per share for which Common Stock is issuable" shall be determined by
dividing (a) the total amount received or receivable by the Corporation as
consideration for the issue or sale of such Convertible Securities, plus the
minimum aggregate amount of additional consideration, if any, payable to the
Corporation upon the conversion or exchange thereof, by (b) the total maximum
number of shares of Common Stock issuable upon the conversion or exchange of all
such Convertible Securities. No further adjustment of the Conversion Price shall
be made when Common Stock is actually issued upon the conversion or exchange of
such Convertible Securities, and if any such issue or sale of such Convertible
Securities is made upon exercise of any Options for which adjustments of the
Conversion Price had been or are to be made pursuant to other provisions of this
Section 6, no further adjustment of the Conversion Price shall be made by reason
of such issue or sale.

          (iii)  Change in Option Price or Conversion Rate.  If the purchase
                 -----------------------------------------
price provided for in any Options, the additional consideration, if any, payable
upon the conversion or exchange of any Convertible Securities or the rate at
which any Convertible Securities are convertible into or exchangeable for Common
Stock changes at any time, the Conversion Price in effect at the time of such
change shall be immediately adjusted to the Conversion Price which would have
been in effect at such time had such Options or Convertible Securities still
outstanding provided for such changed purchase price, additional consideration
or conversion rate, as the case may be, at the time initially granted, issued or
sold.  For purposes of Section 6E, if the terms of any Option or Convertible
Security are changed in the manner described in the immediately preceding
sentence, then such Option or Convertible Security and the Common Stock deemed
issuable upon exercise, conversion or exchange thereof shall be deemed to have
been issued as of the date of such change; provided that no such change shall at
any time cause the Conversion Price hereunder to be increased.

          (iv)   Treatment of Expired Options and Unexercised Convertible
                 --------------------------------------------------------
Securities.  Upon the expiration of any Option or the termination of any right
----------
to convert or exchange any Convertible Security without the exercise of any such
Option or right, the Conversion Price then in effect hereunder shall be adjusted
immediately to the Conversion Price which would have been in effect at the time
of such expiration or termination had such Option or Convertible Security, to
the extent outstanding immediately prior to such expiration or termination,
never been issued; provided that if the Corporation shall accelerate the
expiration of any Option or the termination of any right to convert or exchange
any Convertible Security,  such adjustment shall not be effective until 15 days
after written notice thereof has been given to all holders of the Series C
Preferred.  For purposes of Section 6E, the expiration or termination of any
Option or Convertible Security which was outstanding as of the Closing Date
shall not cause the Conversion Price hereunder to be adjusted unless, and only
to the extent that, a change in the terms of such Option or Convertible Security
caused it to be deemed to have been issued after the Closing Date.

          (v)    Calculation of Consideration Received.  If any Common Stock,
                 -------------------------------------
Option or Convertible Security is issued or sold or deemed to have been issued
or sold for cash, marketable securities or cash equivalents, the consideration
received therefor shall be deemed to be the amount received by the Corporation
therefor (before deducting any expenses, discounts or commissions paid or
incurred in connection with such issue or sale).

                                      -9-
<PAGE>

          (vi)   Integrated Transactions.  In case any Option is issued in
                 -----------------------
connection with the issue or sale of other securities of the Corporation,
together comprising one integrated transaction in which no specific
consideration is allocated to such Option by the parties thereto, the Option
shall be deemed to have been issued for a consideration of $.01.

          (vii)  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 Corporation or any Subsidiary, and the disposition of any
shares so owned or held to any person other than the Corporation or any
Subsidiary shall be considered an issue or sale of Common Stock.

          (viii) Record Date.  If the Corporation takes a record of the
                 -----------
holders of Common Stock for the purpose of entitling them (a) to receive a
dividend or other distribution payable in Common Stock, Options or Convertible
Securities or (b) to subscribe for or purchase Common Stock, Options 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 upon the making of such other
distribution or the date of the granting of such right of subscription or
purchase, as the case may be, unless subsequently abandoned.

     6F.  Subdivision or Combination of Common Stock.  If the Corporation at any
          ------------------------------------------
time subdivides (by any stock split, stock dividend, recapitalization or
otherwise) one or more classes of its outstanding shares of Common Stock into a
greater number of shares, the Conversion Price in effect immediately prior to
such subdivision shall be proportionately reduced, and if the Corporation at any
time combines (by reverse stock split or otherwise) one or more classes of its
outstanding shares of Common Stock into a smaller number of shares, the
Conversion Price in effect immediately prior to such combination shall be
proportionately increased.

     6G.  Corporate Change.  Any recapitalization, reorganization,
          ----------------
reclassification, consolidation, merger or sale of all or substantially all of
the Corporation's assets, in each case which is effected in such a manner that
the holders of Common Stock are entitled to receive (either directly or upon
subsequent liquidation) stock, securities or assets in exchange for Common
Stock, is referred to herein as a "Corporate Change".  Prior to the consummation
of any Corporate Change, the Corporation shall make appropriate provisions to
insure that each of the holders of Series C Preferred shall thereafter have the
right to acquire and receive, in lieu of or in addition to (as the case may be)
the shares of Common Stock immediately theretofore acquirable and receivable
upon the conversion of such holder's Series C Preferred, such shares of stock,
securities or assets as such holder would have received in connection with such
Corporate Change if such holder had converted its Series C Preferred immediately
prior to such Corporate Change.  In each such case, the Corporation shall also
make appropriate provisions to insure that the provisions of this Section 6 and
Sections 7 and 8 hereof shall thereafter be applicable to the Series C Preferred
(including, in the case of any such consolidation, merger or sale in which the
successor entity or purchasing entity is other than the Corporation, an
immediate adjustment of the Conversion Price to the value for the Common Stock
reflected by the terms of such consolidation, merger or sale, and a
corresponding immediate adjustment in the number of shares of Conversion Stock
acquirable and receivable upon conversion of Series C Preferred, if the value so
reflected is less than the Conversion Price in effect immediately prior to such
consolidation, merger or sale).  The Corporation shall not effect any such
consolidation, merger or sale unless, prior to the consummation thereof, the
successor entity (if other than the

                                      -10-
<PAGE>

Corporation) resulting from consolidation or merger or the entity purchasing
such assets assumes by written instrument the obligation to deliver to each such
holder such shares of stock, securities or assets as, in accordance with the
foregoing provisions, such holder may be entitled to acquire. The provisions of
this Section 6G shall not apply in the event of a conversion of the Series C
Preferred pursuant to Section 6B hereof prior to the consummation of the
Corporate Change.

     6H.  Certain Events.  If any event occurs of the type contemplated by the
          --------------
provisions of this Section 6 but not expressly provided for by such provisions,
then the Board shall make an appropriate adjustment in the Conversion Price so
as to protect the rights of the holders of Series C Preferred; provided that no
such adjustment shall increase the Conversion Price as otherwise determined
pursuant to this Section 6 or decrease the number of shares of Conversion Stock
issuable upon conversion of each share of Series C Preferred.

     6I.  Notices.
          -------

          (i)    As promptly as practicable after any adjustment of the
Conversion Price hereunder, the Corporation shall give written notice thereof to
all holders of Series C Preferred, setting forth in reasonable detail and
certifying the calculation and the effective date of such adjustment. In
addition, the Corporation shall give written notice to all holders of Series C
Preferred of any conversion of the Series C Preferred pursuant to Section 6B
hereof within five Business Days after the effective date of such conversion.

          (ii)   The Corporation shall give written notice to all holders of
Series C Preferred at least 15 days prior to the date on which the Corporation
closes its books or takes a record (a) with respect to any dividend or
distribution upon Common Stock or (b) with respect to any pro rata subscription
offer to holders of Common Stock.

          (iii)  The Corporation shall also give written notice to all holders
of Series C Preferred of any proposed Corporate Change at least 20 days prior to
the date on which any Corporate Change is expected to take place.

     6J.  Calculations.  If the amount of any adjustment of the Conversion Price
          ------------
required pursuant to this Section 6 would be less than 1% of the Conversion
Price in effect at the time such adjustment is otherwise so required to be made,
such amount shall be carried forward and an adjustment with respect thereto made
at the time of and together with any subsequent adjustment which, together with
such amount and any other amount or amounts so carried forward, shall aggregate
at least 1% of such Conversion Price.  All calculations under this Section 6
shall be made to the nearest one-tenth of a cent ($.001).

     Section 7.     Liquidating Dividends.
                    ---------------------

     If the Corporation pays a dividend upon the Common Stock payable otherwise
than in cash or other property out of earnings or earned surplus (determined in
accordance with generally accepted accounting principles, consistently applied)
except for a stock dividend payable in shares of Common Stock (a "Liquidating
Dividend"), then the Corporation shall pay to the holders of Series C Preferred
at the time of payment thereof the Liquidating Dividends which would have been
paid

                                      -11-
<PAGE>

on the shares of Conversion Stock had such Series C Preferred been converted
immediately prior to the date on which a record is taken for such Liquidating
Dividend, or, if no record is taken, the date as of which the record holders of
Common Stock entitled to such Liquidating Dividend are to be determined.

     Section 8.     Purchase Rights.
                    ---------------

     If at any time the Corporation grants, issues or sells any Options,
Convertible Securities or rights to purchase stock, warrants, securities or
other property pro rata to the record holders of the Common Stock (the "Purchase
Rights"), then each holder of Series C Preferred shall be entitled to acquire,
upon the terms applicable to such Purchase Rights, the aggregate Purchase Rights
which such holder could have acquired if such holder had held the number of
shares of Conversion Stock acquirable upon conversion of such holder's Series C
Preferred immediately before the date on which a record is taken for the grant,
issuance or sale of such Purchase Rights, or if no such record is taken, the
date as of which the record holders of Common Stock are to be determined for the
grant, issue or sale of such Purchase Rights.

     Section 9.     Event of Noncompliance.
                    ----------------------

     9A.  Definition.  An Event of Noncompliance shall have occurred (i)
          ----------
whenever dividends on the Series C Preferred shall be in arrears in an amount
equal to at least four full quarterly dividends, whether or not consecutive and
whether or not the payment of such dividends is legally permissible or is
prohibited by any agreement to which the Corporation is subject; or (ii) if the
Corporation or any Significant Subsidiary (as defined in Section 11 hereof)
makes an assignment for the benefit of creditors or admits in writing its
inability to pay its debts generally as they become due; or an order, judgment
or decree is entered adjudicating the Corporation or any Significant Subsidiary
bankrupt or insolvent; or any order for relief with respect to the Corporation
or any Significant Subsidiary is entered under the Federal Bankruptcy Code; or
the Corporation or any Significant Subsidiary petitions or applies to any
tribunal for the appointment of a custodian, trustee, receiver or liquidator of
the Corporation or any Significant Subsidiary or of any substantial part of the
assets of the Corporation or any Significant Subsidiary, or commences any
proceeding (other than a proceeding for the voluntary liquidation and
dissolution of a Subsidiary) relating to the Corporation or any Significant
Subsidiary under any bankruptcy, reorganization, arrangement, insolvency,
readjustment of debt, dissolution or liquidation law of any jurisdiction; or any
such petition or application is filed, or any such proceeding is commenced,
against the Corporation or any Significant Subsidiary and either (a) the
Corporation or any such Significant Subsidiary by any act indicates its approval
thereof, consent thereto or acquiescence therein or (b) such petition,
application or proceeding is not dismissed within 90 days.

          The Corporation shall promptly deliver notice of the occurrence of an
Event of Noncompliance to the holders of Series C Preferred upon discovery
thereof.

     9B.  Consequences of Event of Noncompliance.  If an Event of Noncompliance
          --------------------------------------
has occurred and is continuing, the number of directors constituting the Board
shall, at the request of the holders of a majority of the Series C Preferred
then outstanding, be increased by two members, and the holders of the Series C
Preferred shall have the special right, voting separately as a single class

                                      -12-
<PAGE>

(with each Share being entitled to one vote) and to the exclusion of all other
classes of the Corporation's stock, to elect two individuals to fill such newly
created directorships, to fill any vacancies in such directorships and to remove
any individuals elected to such directorships.  The newly created directorships
shall be entitled to the same rights and powers as the other directorships of
the Corporation.  The special right of the holders of Series C Preferred to
elect individuals to fill such directorships, to fill any vacancies in such
directorships and to remove any individuals elected to such directorships may be
exercised at the special meeting called pursuant to this Section 9B, at any
annual or other special meeting of stockholders and, to the extent and in the
manner permitted by applicable law, pursuant to a written consent in lieu of a
stockholders meeting.  Such special right shall continue until such time as
there is no longer any Event of Noncompliance in existence, at which time such
special right shall terminate subject to revesting upon the occurrence and
continuation of any subsequent Event of Noncompliance which gives rise to such
special right hereunder.

          At any time when such special right has vested in the holders of the
Series C Preferred, a proper officer of the Corporation shall, upon the written
request of the holders of at least 10% of the Series C Preferred then
outstanding addressed to the secretary of the Corporation, call a special
meeting of the holders of Series C Preferred for the purpose of electing or
removing directors pursuant to and in accordance with this Section 9B.  Such
meeting shall be held at the earliest legally permissible date at the principal
office of the Corporation, or at such other place designated by the holders of
at least 10% of the Series C Preferred then outstanding.  If such meeting has
not been called by a proper officer of the Corporation within 10 days after
personal service of such written request upon the secretary of the Corporation
or within 20 days after mailing the same to the secretary of the Corporation at
its principal office, then the holders of at least 10% of the Series C Preferred
then outstanding may designate in writing one of their number to call such
meeting at the expense of the Corporation, and such meeting may be called by
such person so designated upon the notice required for annual meetings of
stockholders and shall be held at the Corporation's principal office, or at such
other place designated by the holders of at least 10% of the Series C Preferred
then outstanding.  Any holder of Series C Preferred so designated shall be given
access to the stock record books of the Corporation for the purpose of causing a
meeting of stockholders to be called pursuant to this Section 9B.

          At any meeting or at any adjournment thereof at which the holders of
Series C Preferred have the special right to elect or remove directors, the
presence, in person or by proxy, of the holders of a majority of the Series C
Preferred then outstanding shall be required to constitute a quorum for the
election or removal of any director by the holders of the Series C Preferred
exercising such special right.  The vote of a majority of such quorum shall be
required to elect or remove any such director.

          Any directors so elected by the holders of Series C Preferred shall
continue to serve as directors of the Corporation until the date on which there
is no longer any Event of Noncompliance in existence.  On such date, the number
of directors constituting the Board shall decrease to such number as constituted
the whole Board immediately prior to the occurrence of the Event of
Noncompliance giving rise to the special right to elect directors.

                                      -13-
<PAGE>

          If any Event of Noncompliance exists, each holder of Series C
Preferred shall also have any other rights which such holder is entitled to
under any contract or agreement and any other rights which such holder may have
pursuant to applicable law.

     Section 10.    Record Holders.
                    --------------

     The Corporation shall deem and treat the record holder of any 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 11.    Definitions.
                    -----------

          "Business Day" means any day other than a Saturday, Sunday or a day on
           ------------
which state or federally chartered banking institutions in Dallas, Texas are not
required to be opened.

          "Closing Date" has the meaning given such term in the Stock Purchase
           ------------
Agreement.

          "Common Stock" means, collectively, the Corporation's Common Stock,
           ------------
par value $.01 per share (including any and all Conversion Stock), and any
capital stock of any class of the Corporation hereafter authorized which is not
limited to a fixed sum or percentage of par or stated value in respect to the
rights of the holders thereof to participate in dividends or in the distribution
of assets upon any Liquidation of the Corporation.

          "Common Stock Deemed Outstanding" means, at any given time, the number
           -------------------------------
of shares of Common Stock actually outstanding at such time, plus the number of
shares of Common Stock deemed to be outstanding pursuant to Sections 6E(i) and
6E(ii) hereof whether or not the Options or Convertible Securities are actually
exercisable at such time.

          "Conversion Price" means the conversion price per share of Common
           ----------------
Stock into which the Series C Preferred is convertible, as such conversion price
may be adjusted pursuant to Section 6D hereof.

          "Conversion Stock" means shares of the Corporation's Common Stock,
           ----------------
provided that if there is a change such that the securities issuable upon
conversion of the Series C Preferred are issued by an entity other than the
Corporation or there is a change in the type or class of securities so issuable,
then the term "Conversion Stock" shall mean one share of the security issuable
upon conversion of the Series C Preferred if such security is issuable in
shares, or shall mean the smallest unit in which such security is issuable if
such security is not issuable in shares.

          "Convertible Securities" means any stock or securities directly or
           ----------------------
indirectly convertible into or exchangeable for Common Stock.

          "Junior Securities" means any capital stock or other equity securities
           -----------------
of the Corporation, except for the Series C Preferred.

          "Liquidation Value" of any Share as of any particular date shall be
           -----------------
equal to $25.00.

                                      -14-
<PAGE>

          "Loan Agreements" means all loan or credit agreements or indentures to
           ---------------
which the Corporation is a party at any time.

          "Mandatory Conversion Date" means the third anniversary of the Closing
           -------------------------
Date.

          "Market Price" of any security on any day means the closing price of
           ------------
such security's sales on such day on the principal securities exchange on which
such security may at the time be listed, or, if there were no sales on such
exchange on such day, the average of the highest bid and lowest asked prices on
such exchange at the end of such day, or, if on such day such security is not so
listed, the average of the representative bid and asked prices quoted in the
NASDAQ System as of 4:00 P.M., New York time, on such day, or, if on such day
such security is not quoted in the NASDAQ System, the average of the highest bid
and lowest asked prices on such day in the domestic over-the-counter market as
reported by the National Quotation Bureau, Incorporated, or any similar
successor organization.  If at any time such security is not listed on any
securities exchange or quoted in the NASDAQ System or the over-the-counter
market, the "Market Price" shall be the fair value thereof determined jointly by
the Corporation and the holders of a majority of the outstanding Shares of the
Series C Preferred.  If such parties are unable to reach agreement within a
reasonable period of time, such fair value shall be determined by an independent
appraiser experienced in valuing securities jointly selected by the Corporation
and the holders of a majority of the outstanding Shares of the Series C
Preferred.  The determination of such appraiser shall be final and binding upon
the parties, and the Corporation shall pay the fees and expenses of such
appraiser.  For purposes of this definition, "Market Price" shall include, in
the case of an underwritten public offering or a private offering of securities
that are currently publicly traded, an allowance for a customary discount to the
current market trading price which is determined by the managing underwriter (if
any) and the Corporation to be reasonably required to effect such offering.

          "Options" means any rights, warrants or options to subscribe for or
           -------
purchase Common Stock or Convertible Securities.

          "Significant Subsidiary" means, with respect to any person, a
           ----------------------
Subsidiary constituting a "significant subsidiary" of such person for purposes
of Rule 1-02(w) of Regulation S-X under the Securities Act of 1933, or any
successor provision thereof.

          "Stock Purchase Agreement" means the Amended and Restated Stock
           ------------------------
Purchase Agreement dated as of December 13, 1999, by and between the Corporation
and Wiser Investment Company, LLC, as such agreement may from time to time be
amended in accordance with its terms.

          "Subsidiary" means, with respect to any person, any corporation,
           ----------
limited liability company, partnership, association or other business entity of
which (i) if a corporation, a majority of the total voting power of shares of
stock entitled (without regard to the occurrence of any contingency) to vote in
the election of directors, managers or trustees thereof is at the time owned or
controlled, directly or indirectly, by that person or one or more of the other
Subsidiaries of that person or a combination thereof, or (ii) if a limited
liability company, partnership, association or other business entity, a majority
of the partnership or other similar ownership interests thereof is at the time
owned or controlled, directly or indirectly, by that person or one or more of
the other Subsidiaries of that person or a combination thereof.  For purposes
hereof, a person or persons shall

                                      -15-
<PAGE>

be deemed to have a majority ownership interest in a limited liability company,
partnership, association or other business entity if such person or persons
shall be allocated a majority of limited liability company, partnership,
association or other business entity gains or losses.

          "Warrant Agreement" has the meaning given such term in the Stock
           -----------------
Purchase Agreement.

     Section 12.    Amendment and Waiver.
                    --------------------

     No amendment, modification or waiver of any provision of Sections 1 to 15
of this Certificate of Designations shall be binding or effective without the
prior written consent of the holders of at least two-thirds of the Series C
Preferred outstanding at the time such action is taken; provided that no such
action shall (a) change the rate at which or the manner in which dividends on
the Series C Preferred accrue or the times at which such dividends become
payable, without the prior written consent of the holders of at least 90% of the
Series C Preferred then outstanding, (b) increase the Conversion Price of the
Series C Preferred or decrease the number of shares or class of stock into which
the Series C Preferred is convertible other than as provided under Section 6
hereof, without the prior written consent of the holders of at least 90% of the
Series C Preferred then outstanding or (c) change the percentage required to
approve any change described in clauses (a) and (b) above, without the prior
written consent of the holders of at least 90% of the Series C Preferred then
outstanding.

     Section 13.    Notices.
                    -------

     Except as otherwise expressly provided hereunder, all notices referred to
herein shall be in writing and shall be delivered by first class registered or
certified United States mail or by reputable overnight courier service, charges
prepaid, and shall be deemed to have been given when so mailed or sent (i) to
the Corporation (attention: Secretary) at its principal executive offices and
(ii) to any stockholder, at such holder's address as it appears in the stock
records 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 14.    Acquired Shares.
                    ---------------

     Any Shares of Series C Preferred purchased or otherwise acquired by the
Corporation in any manner whatsoever 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 of the Corporation and
may be reissued as part of a new series of preferred stock to be created by
resolution or resolutions of the Board, subject to the conditions and
restrictions on issuance set forth herein.

     Section 15.    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.

                                      -16-
<PAGE>

                              *     *     *     *

     IN WITNESS WHEREOF, the Corporation has caused this Certificate of
Designations to be signed this 25th day of May, 2000.


                                  THE WISER OIL COMPANY

                                  By: /s/ Andrew J. Shoup, Jr.
                                     -----------------------------------
                                     Name: Andrew J. Shoup, Jr.
                                          ------------------------------
                                     Title: President
                                           -----------------------------

                                      -17-