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                                                                  EXHIBIT 3.1(b)


                           CERTIFICATE OF DESIGNATIONS

                                       OF

                  SERIES A JUNIOR PARTICIPATING PREFERRED STOCK

                                       OF

                          PENNZOIL-QUAKER STATE COMPANY

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

                  PENNZOIL-QUAKER STATE COMPANY, a corporation organized and
existing under the General Corporation Law of the State of Delaware, in
accordance with the provisions of Section 103 thereof, DOES HEREBY CERTIFY:

                  That pursuant to the authority vested in the Board of
Directors in accordance with the provisions of the Restated Certificate of
Incorporation of the said Corporation, the said Board of Directors on December
14, 1998 adopted the following resolution creating a series of 1,000,000 shares
of Preferred Stock designated as "Series A Junior Participating Preferred
Stock":

                  RESOLVED, that pursuant to the authority vested in the Board
         of Directors of this Corporation in accordance with the provisions of
         the Restated Certificate of Incorporation, a series of Preferred Stock,
         par value $1.00 per share, of the Corporation be and hereby is created,
         and that the designation and number of shares thereof and the voting
         and other powers, preferences and relative, participating, optional or
         other rights of the shares of such series and the qualifications,
         limitations and restrictions thereof are as follows:

                  SERIES A JUNIOR PARTICIPATING PREFERRED STOCK

                  1. Designation and Amount. There shall be a series of
Preferred Stock that shall be designated as "Series A Junior Participating
Preferred Stock," and the number of shares constituting such series shall be
1,000,000. Such number of shares may be increased or decreased by resolution of
the Board of Directors; provided, however, that no decrease shall reduce the
number of shares of Series A Junior Participating Preferred Stock to less than
the number of shares then issued and outstanding plus the number of shares
issuable upon exercise of outstanding rights, options or warrants or upon
conversion of outstanding securities issued by the Corporation.

                  2. Dividends and Distributions.

                  (A) Subject to the prior and superior rights of the holders of
any shares of any series of Preferred Stock ranking prior and superior to the
shares of Series A Junior Participating


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Preferred Stock with respect to dividends, the holders of shares of Series A
Junior Participating Preferred Stock, in preference to the holders of shares of
any class or series of stock of the Corporation ranking junior to the Series A
Junior Participating Preferred Stock, shall be entitled to receive, when, as and
if declared by the Board of Directors out of funds legally available for the
purpose, quarterly dividends payable in cash on the 15th day of March, June,
September and December in each year (each such date being referred to herein as
a "Quarterly Dividend Payment Date"), commencing on the first Quarterly Dividend
Payment Date after the first issuance of a share or fraction of a share of
Series A Junior Participating Preferred Stock, in an amount per share (rounded
to the nearest cent) equal to the greater of (a) $2.00 or (b) the Adjustment
Number (as defined below) times the aggregate per share amount of all cash
dividends, and the Adjustment Number times the aggregate per share amount
(payable in kind) of all non-cash dividends or other distributions other than a
dividend payable in shares of Common Stock or a subdivision of the outstanding
shares of Common Stock (by reclassification or otherwise), declared on the
Common Stock, par value $0.10 per share, of the Corporation (the "Common Stock")
since the immediately preceding Quarterly Dividend Payment Date, or, with
respect to the first Quarterly Dividend Payment Date, since the first issuance
of any share or fraction of a share of Series A Junior Participating Preferred
Stock. The "Adjustment Number" shall initially be 100. In the event the
Corporation shall at any time after December 18, 1998 (the "Rights Declaration
Date") (i) declare any dividend on Common Stock payable in shares of Common
Stock, (ii) subdivide the outstanding Common Stock or (iii) combine the
outstanding Common Stock into a smaller number of shares, then in each such case
the Adjustment Number in effect immediately prior to such event shall be
adjusted by multiplying such Adjustment Number by a fraction the numerator of
which is the number of shares of Common Stock outstanding immediately after such
event and the denominator of which is the number of shares of Common Stock that
were outstanding immediately prior to such event.

                  (B) The Corporation shall declare a dividend or distribution
on the Series A Junior Participating Preferred Stock as provided in paragraph
(A) above immediately after it declares a dividend or distribution on the Common
Stock (other than a dividend payable in shares of Common Stock); provided that,
in the event no dividend or distribution shall have been declared on the Common
Stock during the period between any Quarterly Dividend Payment Date and the next
subsequent Quarterly Dividend Payment Date, a dividend of $2.00 per share on the
Series A Junior Participating Preferred Stock shall nevertheless be payable on
such subsequent Quarterly Dividend Payment Date.

                  (C) Dividends shall begin to accrue and be cumulative on
outstanding shares of Series A Junior Participating Preferred Stock from the
Quarterly Dividend Payment Date next preceding the date of issue of such shares
of Series A Junior Participating Preferred Stock, unless the date of issue of
such shares is prior to the record date for the first Quarterly Dividend Payment
Date, in which case dividends on such shares shall begin to accrue from the date
of issue of such shares, or unless the date of issue is a Quarterly Dividend
Payment Date or is a date after the record date for the determination of holders
of shares of Series A Junior Participating Preferred Stock entitled to receive a
quarterly dividend and before such Quarterly Dividend Payment Date, in either of
which events such dividends shall begin to accrue and be cumulative from such
Quarterly


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Dividend Payment Date. Accrued but unpaid dividends shall not bear interest.
Dividends paid on the shares of Series A Junior Participating Preferred Stock in
an amount less than the total amount of such dividends at the time accrued and
payable on such shares shall be allocated pro rata on a share-by-share basis
among all such shares at the time outstanding. The Board of Directors may fix a
record date for the determination of holders of shares of Series A Junior
Participating Preferred Stock entitled to receive payment of a dividend or
distribution declared thereon, which record date shall be no more than 30 days
prior to the date fixed for the payment thereof.

                  3. Voting Rights. The holders of shares of Series A Junior
Participating  Preferred Stock shall have the following voting rights:

                  (A) Each share of Series A Junior Participating Preferred
Stock shall entitle the holder thereof to a number of votes equal to the
Adjustment Number on all matters submitted to a vote of the stockholders of the
Corporation.

                  (B) Except as otherwise provided herein, in the Restated
Certificate of Incorporation or by law, the holders of shares of Series A Junior
Participating Preferred Stock, the holders of shares of any other class or
series entitled to vote with the Common Stock and the holders of shares of
Common Stock shall vote together as one class on all matters submitted to a vote
of stockholders of the Corporation.

                  (C)(i) If at any time dividends on any Series A Junior
Participating Preferred Stock shall be in arrears in an amount equal to six
quarterly dividends thereon, the occurrence of such contingency shall mark the
beginning of a period (herein called a "default period") that shall extend until
such time when all accrued and unpaid dividends for all previous quarterly
dividend periods and for the current quarterly dividend period on all shares of
Series A Junior Participating Preferred Stock then outstanding shall have been
declared and paid or set apart for payment. During each default period, (1) the
number of Directors shall be increased by two, effective as of the time of
election of such Directors as herein provided, and (2) the holders of Preferred
Stock (including holders of the Series A Junior Participating Preferred Stock)
upon which these or like voting rights have been conferred and are exercisable
(the "Voting Preferred Stock") with dividends in arrears in an amount equal to
six quarterly dividends thereon, voting as a class, irrespective of series,
shall have the right to elect such two Directors.

                  (ii) During any default period, such voting right of the
holders of Series A Junior Participating Preferred Stock may be exercised
initially at a special meeting called pursuant to subparagraph (iii) of this
Section 3(C) or at any annual meeting of stockholders, and thereafter at annual
meetings of stockholders, provided that such voting right shall not be exercised
unless the holders of at least one-third in number of the shares of Voting
Preferred Stock outstanding shall be present in person or by proxy. The absence
of a quorum of the holders of Common Stock shall not affect the exercise by the
holders of Voting Preferred Stock of such voting right.

                  (iii) Unless the holders of Voting Preferred Stock shall,
during an existing default period, have previously exercised their right to
elect Directors, the Board of Directors may order,


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or any stockholder or stockholders owning in the aggregate not less than ten
percent of the total number of shares of Voting Preferred Stock outstanding,
irrespective of series, may request, the calling of a special meeting of the
holders of Voting Preferred Stock, which meeting shall thereupon be called by
the Chairman of the Board, the President, a Vice President or the Secretary of
the Corporation. Notice of such meeting and of any annual meeting at which
holders of Voting Preferred Stock are entitled to vote pursuant to this
paragraph (C)(iii) shall be given to each holder of record of Voting Preferred
Stock by mailing a copy of such notice to him at his last address as the same
appears on the books of the Corporation. Such meeting shall be called for a time
not earlier than 20 days and not later than 60 days after such order or request
or, in default of the calling of such meeting within 60 days after such order or
request, such meeting may be called on similar notice by any stockholder or
stockholders owning in the aggregate not less than ten percent of the total
number of shares of Voting Preferred Stock outstanding. Notwithstanding the
provisions of this paragraph (C)(iii), no such special meeting shall be called
during the period within 60 days immediately preceding the date fixed for the
next annual meeting of the stockholders.

                  (iv) In any default period, after the holders of Voting
Preferred Stock shall have exercised their right to elect Directors voting as a
class, (x) the Directors so elected by the holders of Voting Preferred Stock
shall continue in office until their successors shall have been elected by such
holders or until the expiration of the default period, and (y) any vacancy in
the Board of Directors may be filled by vote of a majority of the remaining
Directors theretofore elected by the holders of the class or classes of stock
which elected the Director whose office shall have become vacant. References in
this paragraph (C) to Directors elected by the holders of a particular class or
classes of stock shall include Directors elected by such Directors to fill
vacancies as provided in clause (y) of the foregoing sentence.

                  (v) Immediately upon the expiration of a default period, (x)
the right of the holders of Voting Preferred Stock as a class to elect Directors
shall cease, (y) the term of any Directors elected by the holders of Voting
Preferred Stock as a class shall terminate and (z) the number of Directors shall
be such number as may be provided for in the Restated Certificate of
Incorporation or By-Laws irrespective of any increase made pursuant to the
provisions of paragraph (C) of this Section 3 (such number being subject,
however, to change thereafter in any manner provided by law or in the Restated
Certificate of Incorporation or By-Laws). Any vacancies in the Board of
Directors effected by the provisions of clauses (y) and (z) in the preceding
sentence may be filled by a majority of the remaining Directors.

                  (D) Except as set forth herein, holders of Series A Junior
Participating Preferred Stock shall have no special voting rights and their
consent shall not be required (except to the extent they are entitled to vote
with holders of Common Stock as set forth herein) for taking any corporate
action.

                  4. Certain Restrictions.

                  (A) Whenever quarterly dividends or other dividends or
distributions payable on the Series A Junior Participating Preferred Stock as
provided in Section 2 are in arrears, thereafter


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and until all accrued and unpaid dividends and distributions, whether or not
declared, on shares of Series A Junior Participating Preferred Stock outstanding
shall have been paid in full, the Corporation shall not

                           (i) declare or pay dividends on, make any other
         distributions on, or redeem or purchase or otherwise acquire for
         consideration any shares of stock ranking junior (either as to
         dividends or upon liquidation, dissolution or winding up) to the Series
         A Junior Participating Preferred Stock;

                           (ii) declare or pay dividends on or make any other
         distributions on any shares of stock ranking on a parity (either as to
         dividends or upon liquidation, dissolution or winding up) with the
         Series A Junior Participating Preferred Stock, except dividends paid
         ratably on the Series A Junior Participating Preferred Stock and all
         such parity stock on which dividends are payable or in arrears in
         proportion to the total amounts to which the holders of all such shares
         are then entitled; or

                           (iii) redeem or purchase or otherwise acquire for
         consideration any shares of Series A Junior Participating Preferred
         Stock, or any shares of stock ranking on a parity with the Series A
         Junior Participating Preferred Stock, except in accordance with a
         purchase offer made in writing or by publication (as determined by the
         Board of Directors) to all holders of Series A Junior Participating
         Preferred Stock, or to all such holders and the holders of any such
         shares ranking on a parity therewith, upon such terms as the Board of
         Directors, after consideration of the respective annual dividend rates
         and other relative rights and preferences of the respective series and
         classes, shall determine in good faith will result in fair and
         equitable treatment among the respective series or classes.

                  (B) The Corporation shall not permit any subsidiary of the
Corporation to purchase or otherwise acquire for consideration any shares of
stock of the Corporation unless the Corporation could, under paragraph (A) of
this Section 4, purchase or otherwise acquire such shares at such time and in
such manner.

                  5. Reacquired Shares. Any shares of Series A Junior
Participating Preferred Stock 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 and may be reissued as part of
a new series of Preferred Stock to be created by resolution or resolutions of
the Board of Directors, subject to any conditions and restrictions on issuance
set forth herein.

                  6. Liquidation, Dissolution or Winding Up. (A) Upon any
liquidation (voluntary or otherwise), dissolution or winding up of the
Corporation, no distribution shall be made to the holders of shares of stock
ranking junior (either as to dividends or upon liquidation, dissolution or
winding up) to the Series A Junior Participating Preferred Stock unless, prior
thereto, the holders of shares of Series A Junior Participating Preferred Stock
shall have received $100 per share, plus an amount equal to accrued and unpaid
dividends and distributions thereon, whether or not declared,


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to the date of such payment (the "Series A Liquidation Preference"). Following
the payment of the full amount of the Series A Liquidation Preference, no
additional distributions shall be made to the holders of shares of Series A
Junior Participating Preferred Stock unless, prior thereto, the holders of
shares of Common Stock shall have received an amount per share (the "Common
Adjustment") equal to the quotient obtained by dividing (i) the Series A
Liquidation Preference by (ii) the Adjustment Number. Following the payment of
the full amount of the Series A Liquidation Preference and the Common Adjustment
in respect of all outstanding shares of Series A Junior Participating Preferred
Stock and Common Stock, respectively, holders of Series A Junior Participating
Preferred Stock and holders of shares of Common Stock shall, subject to the
prior rights of all other series of Preferred Stock, if any, ranking prior
thereto, receive their ratable and proportionate share of the remaining assets
to be distributed in the ratio of the Adjustment Number to 1 with respect to
such Series A Junior Participating Preferred Stock and Common Stock, on a per
share basis, respectively.

                  (B) In the event, however, that there are not sufficient
assets available to permit payment in full of the Series A Liquidation
Preference and the liquidation preferences of all other series of Preferred
Stock, if any, that rank on a parity with the Series A Junior Participating
Preferred Stock, then such remaining assets shall be distributed ratably to the
holders of such parity shares in proportion to their respective liquidation
preferences. In the event, however, that there are not sufficient assets
available to permit payment in full of the Common Adjustment, then such
remaining assets shall be distributed ratably to the holders of Common Stock.

                  (C) Neither the merger or consolidation of the Corporation
into or with another corporation nor the merger or consolidation of any other
corporation into or with the Corporation shall be deemed to be a liquidation,
dissolution or winding up of the Corporation within the meaning of this Section
6, but the sale, lease or conveyance of all or substantially all the
Corporation's assets shall be deemed to be a liquidation, dissolution or winding
up of the Corporation within the meaning of this Section 6.

                  7. Consolidation, Merger, etc. In case the Corporation shall
enter into any consolidation, merger, combination or other transaction in which
the shares of Common Stock are exchanged for or changed into other stock or
securities, cash and/or any other property, then in any such case each share of
Series A Junior Participating Preferred Stock shall at the same time be
similarly exchanged or changed in an amount per share equal to the Adjustment
Number times the aggregate amount of stock, securities, cash and/or any other
property (payable in kind), as the case may be, into which or for which each
share of Common Stock is changed or exchanged.

                  8. Redemption. (A) The Corporation, at its option, may redeem
shares of the Series A Junior Participating Preferred Stock in whole at any time
and in part from time to time, at a redemption price equal to the Adjustment
Number times the current per share market price (as such term is hereinafter
defined) of the Common Stock on the date of the mailing of the notice of
redemption, together with unpaid accumulated dividends to the date of such
redemption. The "current per share market price" on any date shall be deemed to
be the average of the closing price per share of such Common Stock for the ten
consecutive Trading Days (as such term is hereinafter


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defined) immediately prior to such date; provided, however, that in the event
that the current per share market price of the Common Stock is determined during
a period following the announcement of (A) a dividend or distribution on the
Common Stock other than a regular quarterly cash dividend or (B) any
subdivision, combination or reclassification of such Common Stock and the
ex-dividend date for such dividend or distribution, or the record date for such
subdivision, combination or reclassification, shall not have occurred prior to
the commencement of such ten Trading Day period, then, and in each such case,
the current per share market price shall be properly adjusted to take into
account ex-dividend trading. The closing price for each day shall be the last
sales price, regular way, or, in case no such sale takes place on such day, the
average of the closing bid and asked prices, regular way, in either case as
reported in the principal transaction reporting system with respect to
securities listed or admitted to trading on the New York Stock Exchange, or, if
the Common Stock is not listed or admitted to trading on the New York Stock
Exchange, on the principal national securities exchange on which the Common
Stock is listed or admitted to trading, or, if the Common Stock is not listed or
admitted to trading on any national securities exchange but sales price
information is reported for such security, as reported by the National
Association of Securities Dealers, Inc. Automated Quotations System ("NASDAQ")
or such other self-regulatory organization or registered securities information
processor (as such terms are used under the Securities Exchange Act of 1934, as
amended) that then reports information concerning the Common Stock, or, if sales
price information is not so reported, the average of the high bid and low asked
prices in the over-the-counter market on such day, as reported by NASDAQ or such
other entity, or, if on any such date the Common Stock is not quoted by any such
entity, the average of the closing bid and asked prices as furnished by a
professional market maker making a market in the Common Stock selected by the
Board of Directors of the Corporation. If on any such date no such market maker
is making a market in the Common Stock, the fair value of the Common Stock on
such date as determined in good faith by the Board of Directors of the
Corporation shall be used. The term "Trading Day" shall mean a day on which the
principal national securities exchange on which the Common Stock is listed or
admitted to trading is open for the transaction of business, or, if the Common
Stock is not listed or admitted to trading on any national securities exchange
but is quoted by NASDAQ, a day on which NASDAQ reports trades, or, if the Common
Stock is not so quoted, a Monday, Tuesday, Wednesday, Thursday or Friday on
which banking institutions in the State of New York are not authorized or
obligated by law or executive order to close.

                  (B) In the event that fewer than all the outstanding shares of
the Series A Junior Participating Preferred Stock are to be redeemed, the number
of shares to be redeemed shall be determined by the Board of Directors and the
shares to be redeemed shall be determined by lot or pro rata as may be
determined by the Board of Directors or by any other method that may be
determined by the Board of Directors in its sole discretion to be equitable.

                  (C) Notice of any such redemption shall be given by mailing to
the holders of the shares of Series A Junior Participating Preferred Stock to be
redeemed a notice of such redemption, first class postage prepaid, not later
than the fifteenth day and not earlier than the sixtieth day before the date
fixed for redemption, at their last address as the same shall appear upon the
books of the Corporation. Each such notice shall state: (i) the redemption date;
(ii) the number of shares to be redeemed and, if fewer than all the shares held
by such holder are to be redeemed, the number of


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such shares to be redeemed from such holder; (iii) the redemption price; (iv)
the place or places where certificates for such shares are to be surrendered for
payment of the redemption price; and (v) that dividends on the shares to be
redeemed will cease to accrue on the close of business on such redemption date.
Any notice that is mailed in the manner herein provided shall be conclusively
presumed to have been duly given, whether or not the stockholder received such
notice, and failure duly to give such notice by mail, or any defect in such
notice, to any holder of Series A Junior Participating Preferred Stock shall not
affect the validity of the proceedings for the redemption of any other shares of
Series A Junior Participating Preferred Stock that are to be redeemed. On or
after the date fixed for redemption as stated in such notice, each holder of the
shares called for redemption shall surrender the certificate evidencing such
shares to the Corporation at the place designated in such notice and shall
thereupon be entitled to receive payment of the redemption price. If fewer than
all the shares represented by any such surrendered certificate are redeemed, a
new certificate shall be issued representing the unredeemed shares.

                  (D) The shares of Series A Junior Participating Preferred
Stock shall not be subject to the operation of any purchase, retirement or
sinking fund.

                  9. Ranking. The Series A Junior Participating Preferred Stock
shall rank junior to all other series of the Corporation's Preferred Stock as to
the payment of dividends and the distribution of assets, unless the terms of any
such series shall provide otherwise, and shall rank senior to the Common Stock
as to such matters.

                  10. Amendment. At any time that any shares of Series A Junior
Participating Preferred Stock are outstanding, the Restated Certificate of
Incorporation of the Corporation shall not be amended in any manner which would
materially alter or change the powers, preferences or special rights of the
Series A Junior Participating Preferred Stock so as to affect them adversely
without the affirmative vote of the holders of two-thirds or more of the
outstanding shares of Series A Junior Participating Preferred Stock, voting
separately as a class.

                  11. Fractional Shares. Series A Junior Participating Preferred
Stock may be issued in fractions of a share that shall entitle the holder, in
proportion to such holder's fractional shares, to exercise voting rights,
receive dividends, participate in distributions and to have the benefit of all
other rights of holders of Series A Junior Participating Preferred Stock.

                  IN WITNESS WHEREOF, the undersigned has executed this
Certificate and does affirm the foregoing as true this 29th day of December,
1998.



                                            /s/ LINDA F. CONDIT
                                            ------------------------------------
                                            Linda F. Condit
                                            Vice President