<PAGE>
                                                                     EXHIBIT 3.6

                             PLAINS RESOURCES INC.

        Certificate of Designation, Preferences and Rights of a
        Series of Preferred Stock by Resolution of the Board of
        Directors Providing for an Issue of 175,000 Shares of
        Preferred Stock Designated "SERIES H CONVERTIBLE
        PREFERRED STOCK"


     Plains Resources Inc., a Delaware corporation (hereinafter called the
"Company"), pursuant to the provisions of Section 151 of the General Corporation
Law of the State of Delaware does hereby state and certify that pursuant to the
authority expressly vested in the Board of Directors of the Company by the
Second Restated Certificate of Incorporation, as amended (the "Certificate of
Incorporation"), the Board of Directors, at a meeting thereof duly called and
held on November 28, 2000, at which meeting a quorum was present and acting
throughout, duly adopted the following resolutions providing for the issue of
shares of Preferred Stock hereinafter referred to, and further providing with
respect to such issue of shares of Preferred Stock for such powers,
designations, preferences and relative, participating, optional and other
special rights, and the qualifications, limitations or restrictions thereof, as
are hereinafter set forth, in addition to those set forth in said Certificate of
Incorporation;

      NOW, THEREFORE, BE IT RESOLVED, that  the Board of Directors hereby
provides for the issue of the Series H Preferred Stock;

     RESOLVED, that the powers, designations, preferences and relative,
participating, optional and other special rights, and the qualifications,
limitations or restrictions thereof, of the shares of the Series H Convertible
Preferred Stock shall be as follows:

     Section 1.  Designation and Rank.  The designation of the series of
Preferred Stock created by this resolution shall be "Series H Convertible
Preferred Stock" (hereinafter called this "Series"), and the number of shares
constituting this Series shall be 175,000.  Shares of this Series shall have a
stated value of $500 per share.  The number of authorized shares of this Series
may be reduced by further resolution duly adopted by the Board and by the filing
of a certificate pursuant to the provisions of the General Corporation Law of
the State of Delaware stating that such reduction has been so authorized, but
the number of authorized shares of this Series shall not be increased.  The
shares of this Series shall rank prior to the Junior Stock (as defined in
Section 9) as to distribution of assets.  The shares of this Series shall be of
equal rank as to distribution of assets with all other series of Preferred
Stock, except as provided in a certificate of designation with regard to such
other series of Preferred Stock filed pursuant to Section 151 of the General
Corporation Law of the State of Delaware with the Secretary of State of the
State of Delaware.

     Section 2.  No Dividend Right.  Shares of this Series shall have no rights
to payment of dividends or other distributions in cash, stock or other property.

                                       1
<PAGE>

     Section 3.  No Redemption Right.  Shares of this Series shall not be
subject to any redemption or exchange rights of the Company.

     Section 4.  Voting.

     (a)  Except as otherwise required by law, the holders of shares of this
Series shall not have any right or power to vote on any question or in any
proceeding or to be represented at or to receive notice of any meeting of
holders of capital stock of the Company.  On any matters on which the holders of
shares of this Series shall be entitled to vote, they shall be entitled to one
vote for each share held.

     (b) So long as any shares of this Series remain outstanding, the
affirmative vote or consent of the holders of a majority of the shares of this
Series outstanding at the time, given in person or by proxy, either in writing
or at a meeting, shall be necessary to permit, effect or validate (i) the
authorization, creation or issuance, or any increase in the authorized or issued
amount, of any class or series of Senior Stock and (ii) the amendment,
alteration or repeal of any of the provisions of the Certificate of
Incorporation which would materially and adversely affect any right, preference,
privilege or voting power of shares of this Series or of the holders thereof in
a manner disproportionate to the effect thereof on the holders of any other
shares of the Company's capital stock. However, the creation and issuance of
other series of Parity Stock or Junior Stock shall not be deemed to affect
materially and adversely said rights, preferences, privileges or voting power.

     (c) So long as at least 10,000 shares of this Series remain outstanding,
the holders of shares of this Series outstanding at the time shall be entitled
to vote to permit, effect or validate the authorization of a merger or
consolidation of the Company or any compulsory shares exchange pursuant to which
the Common Stock is converted into other securities, cash or property.  The
holders of shares of this Series shall be entitled to that number of votes equal
to the number of whole shares of Common Stock into which all shares of this
Series held by such holders could be converted pursuant to the provisions of
Section 6 hereof, at the record date for the determination of the stockholders
entitled to vote on such matters or, if no record date is established, at the
day prior to the date such vote is taken or any written consent of stockholders
is first executed, such votes to be counted together with all other shares of
capital stock having general voting powers and not separately as a class.

     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 this Series shall each be entitled to receive out of the
assets of the Company, whether such assets are capital or surplus, for each
share of this Series the sum of $500.00 before any distribution shall be made to
the holders of Junior Stock of the Company, and if the assets of the Company
shall be insufficient to pay in full such amounts, then such assets shall be
distributed among such holders 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. In the event of any complete
liquidation, dissolution or winding-up of the Company, whether voluntary or
involuntary, the holders of shares of this Series shall not be entitled to
receive the liquidation price of such shares held by them until the liquidation
price of all Senior Stock shall have been paid in full.

                                       2
<PAGE>

     Section 6.  Conversion.

     (a)  All outstanding shares of this Series shall be converted into shares
of Common Stock in accordance with this Section 6(a) on September 30, 2001.
Prior to such date, each share of this Series shall be convertible at the option
of the record holder thereof by presentation of the certificate representing
such share by the record holder in person or by registered mail, return receipt
requested with postage prepaid thereon, at the principal office of the Company,
and at such other offices, if any, as the Board of Directors may determine, into
the number of shares of fully paid and nonassessable shares of Common Stock
determined by dividing $500.00 by the Conversion Price in effect at the time of
conversion.

     (b)  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 this Series as herein provided, free from
preemptive rights or any other actual or contingent purchase rights of Persons
other than the holders of shares of this Series, such number of shares of Common
Stock as shall then be issuable upon the conversion of all outstanding shares of
this Series. 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.  Adjustment of Conversion Price.

     (a)  The Conversion Price initially shall be $15.00 (the "Conversion
Price").  The Conversion Price shall be subject to adjustment from time to time
as follows:

          (i)  If the Company, at any time while any shares of this Series are
     outstanding, shall (A) pay a stock dividend or stock dividends or otherwise
     make a distribution or distributions on shares of its capital stock payable
     in shares of Common Stock (or in securities convertible into shares of
     Common Stock), (B) except as set forth in clause (A) above, pay a stock
     dividend or make a distribution on shares of its capital stock payable in
     shares of its capital stock of any class other than Common Stock or a class
     convertible into Common Stock, (C) subdivide outstanding shares of Common
     Stock into a larger number of shares, (D) combine outstanding shares of
     Common Stock into a smaller number of shares, or (E) issue by
     reclassification of shares of Common Stock any shares of capital stock of
     the Company of any class or classes, the Conversion Price in effect
     immediately prior to such action shall be adjusted so that the holder of
     any shares of this Series thereafter surrendered for conversion or
     exchanged shall be entitled to receive the number and class or classes of
     shares of the capital stock of the Company which he would have owned or
     have been entitled to receive immediately after the happening of any of the
     events described above, had such shares of this Series been converted or
     exchanged on or immediately prior to the record date for such dividend or
     distribution or the effective date of such subdivision, combination or
     reclassification, as the case may be. Notwithstanding the foregoing, no
     adjustment in the Conversion Price shall be made by reason of the payment
     of dividends on shares of Preferred Stock in additional shares of Preferred
     Stock. An adjustment made pursuant to this subsection 7(a)(i) shall become
     effective immediately after the record date in the case of a dividend or
     distribution and shall become effective immediately after the effective
     date in the case of a subdivision, combination or reclassification.

                                       3
<PAGE>

          (ii) In case the Company, at any time while any shares of this Series
     are outstanding, shall issue rights or warrants to all holders of Common
     Stock entitling them (for a period expiring within 45 days after the record
     date mentioned below) to subscribe for or purchase shares of Common Stock
     at a price per share less than the then Per Share Market Value of Common
     Stock at the record date mentioned below, the Conversion Price shall be
     reduced by multiplying the Conversion Price, as the case may be, in effect
     prior to such record date by a fraction, of which the denominator shall be
     the number of shares of Common Stock (excluding treasury shares, if any)
     outstanding on the date of issuance of such rights or warrants plus the
     number of additional shares of Common Stock offered for subscription or
     purchase, and of which the numerator shall be the number of shares of
     Common Stock (excluding treasury shares, if any) outstanding on the date of
     issuance of such rights or warrants plus the number of shares which the
     aggregate offering price of the total number of shares so offered would
     purchase at such Per Share Market Value. Such adjustment shall be made
     whenever such rights or warrants are issued, and shall become effective
     immediately after the record date for the determination of stockholders
     entitled to receive such rights or warrants. However, upon the expiration
     of any right or warrant to purchase Common Stock the issuance of which
     resulted in an adjustment in the Conversion Price pursuant to this
     subsection 7(a)(ii), if any such right or warrant shall expire and shall
     not have been exercised, the Conversion Price shall immediately upon such
     expiration, be recomputed and effective immediately upon such expiration be
     increased to the prices which they would have been (but reflecting any
     other adjustments in the Conversion Price made pursuant to the provisions
     of this Section 7 after the issuance of such rights or warrants) had the
     adjustment of the Conversion Price made upon the issuance of such rights or
     warrants been made on the basis of offering for subscription or purchase
     only that number of shares of Common Stock actually purchased upon the
     exercise of such rights or warrants actually exercised.

          (iii) In case the Company, at any time while shares of this Series are
     outstanding, shall distribute to all holders of Common Stock evidences of
     its indebtedness or assets (excluding cash dividends or cash distributions
     paid out of earned surplus) or rights or warrants to subscribe for or
     purchase any security (excluding those referred to in subsection 7(a)(ii)
     above) then in each such case the Conversion Price shall be determined by
     multiplying the Conversion Price, as the case may be, in effect prior to
     the record date fixed for determination of stockholders entitled to receive
     such distribution by a fraction, of which the denominator shall be the Per
     Share Market Value of Common Stock determined as of the record date
     mentioned above, and of which the numerator shall be such Per Share Market
     Value of the Common Stock, less the then fair market value (as determined
     by the Board of Directors of the Company in good faith, whose determination
     shall be conclusive if made in good faith; provided, however, that in the
     event of a distribution or series of related distributions exceeding 10% of
     the net assets of the Company, then such fair market value shall be
     determined by a nationally recognized or major regional investment banking
     firm or firm of independent certified public accountants of recognized
     standing (which may be the firm that regularly examines the financial
     statements of the Company) selected in good faith by the Board of Directors
     of the Company, and in either case shall be described in a statement
     provided to all registered holders of this Series) of the portion of assets
     or evidences of indebtedness so distributed or such subscription rights
     applicable to one share

                                       4
<PAGE>

     of Common Stock. Such adjustment shall be made whenever any such
     distribution is made and shall become effective immediately after the
     record date mentioned above.

          (iv) If the Company, at any time while any shares of this Series are
     outstanding, shall issue or sell shares of Common Stock (excluding stock
     issuances referred to in other provisions of this Section 7(a)) for a
     consideration per share which is less than the Per Share Market Value of
     Common Stock on the date of such issuance or sale, the Conversion Price
     shall be reduced by multiplying the Conversion Price in effect immediately
     prior to the date of such issuance or sale by a fraction, of which the
     denominator shall be the number of shares of Common Stock (excluding
     treasury shares, if any) outstanding on the date of such issuance or sale
     plus the number of additional shares of Common Stock issued or sold, and of
     which the numerator shall be the number of shares of Common Stock
     (excluding treasury shares, if any) outstanding on the date of such
     issuance or sale plus the number of shares which the aggregate
     consideration received or receivable by the Company for the total number of
     shares so issued or sold would purchase at such Per Share Market Value.
     Such adjustment shall be made whenever such shares are issued, and shall
     become effective immediately after such issuance. If the consideration
     received or receivable by the Company for such issuance or sale of shares
     of Common Stock is not cash, the fair market value of such consideration
     shall be determined by the Board, an investment banking firm, or certified
     public accountants in the manner specified in subsection 7(b).

          (v)  If the Company, at any time while any shares of this Series are
     outstanding, shall issue rights, options, or warrants (excluding those
     referred to in other provisions of this Section 7(a)) which entitle the
     holders thereof to purchase shares of Common Stock (such rights, options,
     or warrants collectively referred to as "Purchase Rights") at a price per
     share less than the then Per Share Market Value of Common Stock on the date
     of the issuance of such Purchase Rights, the Conversion Price shall be
     reduced by multiplying the Conversion Price in effect immediately prior to
     the date of issuance of such Purchase Rights by a fraction, of which the
     denominator shall be the number of shares of Common Stock (excluding
     treasury shares, if any) outstanding on the date of issuance of such
     Purchase Rights plus the number of additional shares of Common Stock
     offered for purchase, and of which the numerator shall be the number of
     shares of Common Stock (excluding treasury shares, if any) outstanding on
     the date of issuance of such Purchase Rights plus the number of shares
     which the aggregate consideration received or receivable by the Company in
     connection with the grant as well as the exercise of such Purchase Rights
     would purchase at such Per Share Market Value. Such adjustment shall be
     made whenever such Purchase Rights are issued, and shall become effective
     immediately after the issuance of such Purchase Rights. However, upon the
     expiration of any such Purchase Right the issuance of which resulted in an
     adjustment in the Conversion Price pursuant to this subsection 7(a)(v), if
     such Purchase Right shall not have been fully exercised, the Conversion
     Price shall immediately upon such expiration be recomputed and effective
     immediately upon such expiration be increased to the prices which they
     would have been (but reflecting any other adjustments in the Conversion
     Price made pursuant to the provisions of this Section 7 after the issuance
     of such Purchase Rights) had the adjustment of the Conversion Price made
     upon the issuance of such Purchase Right been made on the basis of offering
     for purchase only that number of shares of Common Stock actually purchased
     upon the exercise of such Purchase

                                       5
<PAGE>

     Rights which were actually exercised. If the consideration for the Purchase
     Rights received or receivable by the Company for the grant or exercise of
     such Purchase Rights is not cash, the fair market value of such
     consideration shall be determined by the Board, an investment banking firm,
     or certified public accountants in the manner specified in subsection 7(b).

          (vi) No notification to the holders of any adjustment in the
     Conversion Price otherwise required by this Section 7 shall be required
     unless such adjustment would require an increase or decrease of at least 1%
     in such price; provided, however, that any adjustment which by reason of
     this subsection 7(a)(vi) is not required to be made shall be carried
     forward and taken into account in any subsequent adjustments, and that upon
     presentment of shares of this Series for conversion, all adjustments shall
     be made calculating the conversion rights of such holder. All calculations
     under this Section 7 shall be made to the nearest cent or the nearest
     1/100th of a share, as the case may be.

          (vii) Whenever the Conversion Price is adjusted, as herein provided,
     the Company shall promptly mail to each registered holder of shares of this
     Series a notice setting forth the Conversion Price after such adjustment
     and setting forth a brief statement of facts requiring such adjustment.
     Such notice prepared in good faith shall be conclusive evidence of the
     correctness of such adjustment absent manifest error.

          (viii) In case of any reclassification of the Common Stock, any
     consolidation or merger of the Company with or into another person, sale or
     transfer of all or substantially all of the assets of the Company or any
     compulsory share exchange pursuant to which share exchange the Common Stock
     is converted into other securities, cash or property, then the holders of
     the shares of this Series then outstanding 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 reclassification, consolidation, merger, sale, transfer or
     share exchange by a holder of a number of shares of the Common Stock of the
     Company into which such shares of this Series could have been converted
     immediately prior to such reclassification, consolidation, merger, sale,
     transfer or share exchange.

     This provision shall similarly apply to successive reclassifications,
     consolidations, mergers, sales, transfers or share exchanges.

          (ix) In case:

                    (A)  the Company shall declare a dividend (or any other
               distribution) on the Common Stock payable otherwise than in cash
               out of its earned surplus; or

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

                                       6
<PAGE>

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

                    (D)  the approval of any stockholders of the Company shall
               be required in connection with any reclassification of the Common
               Stock of the Company (other than a subdivision or combination of
               the outstanding shares of Common Stock), any consolidation or
               merger to which the Company is a party, any sale or transfer of
               all or substantially all of the assets of the Company, or any
               compulsory share exchange whereby the Common Stock is converted
               into other securities, cash or property, or

                    (E)  of the voluntary or involuntary dissolution,
               liquidation or winding up of the affairs of the Company; then the
               Company shall cause to be filed at each office or agency
               maintained for the purpose of conversion of the shares of this
               Series, and shall cause to be mailed to the holders of record of
               the shares of this Series at their last addresses as they shall
               appear upon the stock books of the Company, at least 10 days
               prior to the applicable record date hereinafter specified, a
               notice stating (x) the date on which a record is to be taken for
               the purpose of such dividend, distribution, redemption, rights or
               warrants, or, if a record is not to be taken, the date as of
               which the holders of Common Stock of record to be entitled to
               such dividend, distribution, redemption, rights or warrants are
               to be determined, or (y) the date on which such reclassification,
               consolidation, merger, sale, transfer, share exchange,
               dissolution, liquidation or winding up is expected to become
               effective, and the date as of which it is expected that holders
               of Common Stock of record shall be entitled to exchange their
               shares of Common Stock for securities or other property
               deliverable upon such reclassification, consolidation, merger,
               sale, transfer, share exchange, dissolution, liquidation or
               winding up (but no failure to mail such notice or any defect
               therein or in the mailing thereof shall affect the validity of
               the corporate action required to be specified in such notice).

     (b)  In case at any time conditions shall arise by reason of action taken
by the Company, which, in the opinion of the Board of Directors of the Company,
are not adequately covered by the other provisions hereof and which might
materially and adversely affect the rights of the holders of shares of this
Series, or in case at any time any such conditions are expected to arise by
reason of any action contemplated by the Company, the Board of Directors of the
Company shall appoint a nationally recognized or major regional investment
banking firm or a firm of independent certified public accountants of recognized
standing (which may be the firm that regularly examines the financial statements
of the Company), who shall give their opinion as to the adjustment, if any (not
inconsistent with the standards established in this Section 7), of the
Conversion Price (including, if necessary, any adjustment as to the securities
into which shares of this Series may thereafter be convertible or exchangeable)
which is or would be required to preserve without dilution the rights of the
holders of shares of this Series. The Board of Directors of the Company shall
make the adjustment recommended forthwith upon the receipt of such opinion or
the taking of any such action

                                       7
<PAGE>

contemplated, as the case may be; provided, however, that no such adjustment of
the Conversion Price shall be made which in the opinion of the investment
banking firm or firm of accountants giving the aforesaid opinion would result in
an increase of the Conversion Price to more than the Conversion Price then in
effect.

     Section 8.  Fractional Shares; Transfer Taxes; HSR Act.

     (a)  The Company shall not be required to issue stock certificates
representing fractions of shares of Common Stock, but may, if otherwise
permitted, make a cash payment in respect of any final fraction of a share based
on the Per Share Market Value at such time.  If the Company elects not, or is
unable, to make such a cash payment, the holder of a share of this Series shall
be entitled to receive, in lieu of the final fraction of a share, one whole
share of Common Stock.

     (b)  The issuance of certificates for shares of Common Stock on conversion
of this Series shall be made without charge to the holders thereof for any
documentary stamp or similar taxes that may be payable in respect of the issue
or delivery of such certificate, provided, that the Company shall not be
required to pay any tax that 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 holder of the shares of this Series converted and the Company shall not
be required to issue or deliver such certificates unless or until the person or
persons requesting the issuance thereof shall have paid to the Company the
amount of such tax or shall have established to the satisfaction of the Company
that such tax has been paid.

     (c)  The exercise by a holder of shares of this Series of the conversion
rights granted in Section 6 is subject in all respects to and conditioned upon
compliance by the parties with the HSR Act, and rules and regulations
promulgated pursuant thereto, to the extent that said act, rules and regulations
are applicable to such exercise. The Company and such holder agree to make such
filings with and provide such information to the Federal Trade Commission and
the Department of Justice with respect to such exercise as are required in
connection with the HSR Act in a timely manner and to join each others request
for early termination. The Company and such holder will use such reasonable
efforts to obtain all governmental approval required to permit such exercise and
to cause early termination of the waiting period under the HSR Act.

     Section 9.  Definitions.  For the purposes hereof, the following terms
shall have the following respective meanings:

          "Common Stock" means shares now or hereafter authorized of the class
     of Common Stock, $.10 par value, of the Company presently authorized and
     stock of any other class into which such shares may hereafter have been
     reclassified or changed.

          "Conversion Price" has the meaning given such term in Section 7(a).

          "Junior Stock" means the Common Stock of the Company and any other
     stock of the Company over which shares of this Series has a preference as
     to distribution of assets.

                                       8
<PAGE>

          "Parity Stock" means any stock of the Company ranking as to
     distribution of assets on a parity with this Series.

          "Per Share Market Value" means on any particular date (a) the last
     sale 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, or (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 National 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, or (c) if the Common Stock
     is not quoted on the Nasdaq National Market, the final bid price for a
     share of Common Stock in the over-the-counter market as reported by the
     National Quotation Bureau Incorporated (or any similar organization or
     agency succeeding to its functions of reporting prices), or (d) if the
     Common Stock is no longer publicly traded, as determined by a nationally
     recognized or major regional investment banking firm or firm of independent
     certified public accountants of recognized standing (which may be the firm
     that regularly examines the financial statements of the Company) selected
     in good faith by the Board of Directors of the Company, 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.

          "Person" means a corporation, an association, a partnership, an
     organization, a business, an individual, a government or political
     subdivision thereof or a governmental agency.

          "Preferred Stock" means the Company's Preferred Stock, $1.00 par
     value.

          "Senior Stock" means any shares or class of the Company that are by
     their terms expressly given priority over this Series as to distribution of
     assets on any liquidation of the Company.

                                       9
<PAGE>

     IN WITNESS WHEREOF, said Plains Resources Inc. has caused this Certificate
to be signed by a duly authorized officer, this 4th day of December, 2000.

                              PLAINS RESOURCES INC.


                                           By:    /s/ Phil Kramer
                                                ------------------------------
                                           Name: Phil Kramer
                                           Title:   Executive Vice President and
                                                    Chief Financial Officer

ATTEST:


By:   /s/ Tim Moore
   ----------------------------------
Name:  Tim Moore
Title: Secretary

                                       10