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                                                                     EXHIBIT 3.7

                           CERTIFICATE OF DESIGNATIONS
                                       OF
                      SERIES G1 CONVERTIBLE PREFERRED STOCK
                                       OF
                            HARKEN ENERGY CORPORATION

     Harken Energy Corporation, a Delaware corporation, DOES HEREBY CERTIFY:

     That, pursuant to the authority conferred upon the Board of Directors of
said corporation by virtue of its certificate of incorporation as amended and in
accordance with Section 151 of the General Corporation Law of the State of
Delaware (the "DGCL"), said Board of Directors has duly adopted a resolution at
a special meeting of the Board of Directors held on August 25, 2000, providing
for the issuance of a series of preferred stock, par value $1.00 per share,
designated as Series G1 Convertible Preferred Stock, which resolution reads as
follows:

     "RESOLVED, that the Board of Directors (the "Board of Directors") of Harken
Energy Corporation (the "Corporation") hereby authorizes the issuance of a
series of preferred stock and fixes its designation, powers, preferences and
relative, participating, optional or other special rights, and qualifications,
limitations and restrictions thereof, as follows:

     Section 1.  Designation. The distinctive serial designation of said series
shall be "Series G1 Convertible Preferred Stock" (hereinafter called "Series G1
Preferred Stock"). Each share of Series G1 Preferred Stock shall be identical in
all respects with all other shares of Series G1 Preferred Stock.

     Section 2.  Number of Shares. The number of authorized shares of Series G1
Preferred Stock shall be, in aggregate, 200,000 shares. The number of authorized
shares of Series G1 Preferred Stock may be increased or reduced by the Board of
Directors of the Corporation by the filing of a certificate pursuant to the
provisions of the DGCL stating that the change has been so authorized. When
shares of Series G1 Preferred Stock are purchased or otherwise acquired by the
Corporation or converted into Common Stock, par value $0.01 per share, of the
Corporation (the "Common Stock"), the Corporation shall take all necessary
action to cause the shares of Series G1 Preferred Stock so purchased or acquired
to be canceled and reverted to authorized but unissued shares of Series G1
Preferred Stock undesignated as to series.

     Section 3.  Rank. The Series G1 Preferred Stock shall, with respect to
dividend rights and rights on liquidation, winding-up and dissolution, rank (i)
junior to all claims of creditors, including holders of the Corporation's
outstanding debt securities, (ii) junior to all obligations of the Corporation's
Subsidiaries (as defined in Section 13 below), (iii) senior to all classes of
Common Stock and to each other class of preferred stock established hereafter by
the Board of Directors of the Corporation, the terms of which expressly provide
that it ranks junior to the Series G1 Preferred Stock as to dividend rights and
rights on liquidation, winding-up and dissolution of the Corporation
(collectively referred to, together with all classes of Common

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Stock of the Corporation, as "Junior Stock"), and (iv) on a parity with each
other class of preferred stock established or issued hereafter by the Board of
Directors of the Corporation the terms of which expressly provide that such
class or series shall rank on a parity with the Series G1 Preferred Stock as to
dividend rights and rights on liquidation, winding-up and dissolution
(collectively referred to as "Parity Stock"). The Corporation may authorize the
issuance of any amount of Parity Stock (which may provide for the payment of
dividends in additional shares of Parity Stock in lieu of cash dividends)
without the approval of the holders of the Series G1 Preferred Stock.

     Section 4.  Dividends.

     (a)     The holders of record, as of the Record Date therefor, of the
outstanding shares of Series G Preferred Stock shall be entitled to receive,
when, as and if declared by the Board of Directors of the Corporation, out of
funds legally available therefor, dividends on the Series G Preferred Stock at
an annual rate equal to $8.00 per share (equivalent to 8% of the liquidation
preference annually), payable semi-annually in arrears in cash or, at the option
of the Corporation, in Freely Tradeable shares of the Corporation's Common
Stock. If and when the Corporation shall elect from time to time to pay such
dividends in shares of Common Stock, such shares will be valued at $1.25 per
share; provided, however, that the Corporation may elect to pay such dividends
in shares of the Corporation's Common Stock only if such shares of Common Stock
would upon issuance be Freely Tradeable (as defined in Section 13 below) by the
Corporation; and, provided further, that (i) if the outstanding shares of Common
Stock shall be subdivided into a greater number of shares of Common Stock, such
$1.25 per share valuation shall be proportionately reduced on the day upon which
such subdivision becomes effective, and (ii) if the outstanding shares of Common
Stock shall be combined into a smaller number of shares of Common Stock, such
$1.25 per share valuation shall be proportionately increased on the day such
combination becomes effective. In case the Corporation shall take any action
affecting the Common Stock, other than the aforementioned adjustments, which in
the Board of Directors would materially adversely affect the conversion right of
the holders of the shares of Series G Preferred Stock, such $1.25 valuation may
be adjusted, to the extent permitted by law, in such manner, if any, and at such
time, as the Board of Directors may determine to be equitable in the
circumstances; provided, however, that in no event shall the Board of Directors
be required to take such action.

     (b)     All dividends shall be cumulative, whether or not earned or
declared, and shall accrue from the date of issuance of the Series G1 Preferred
Stock and shall be payable semi-annually in arrears, when, as and if declared by
the Board of Directors. Such dividends will be payable on December 30 and June
30 of each year (a "Dividend Payment Date"), commencing on June 30, 2001;
provided, however, that if a Dividend Payment Date is not a Stock Exchange
Business Day, then the dividend shall be payable on the first immediately
succeeding Stock Exchange Business Day. Dividends shall be paid to the holders
of record of the Series G1 preferred Stock as their names appear on the stock
transfer records of the Corporation on the date designated by the Board of
Directors ("Record Date"), provided, however, that such Record Date may not
precede the date upon which the resolution fixing the Record Date is adopted,
and which Record Date may not be more than sixty (60) days prior to the Dividend
Payment Date. The amount of the dividends payable on the Series G1 Preferred
Stock for each semi-annual

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dividend period shall be computed by dividing by two (2) the annual rate per
share set forth in subsection (a) above. Dividends shall be computed on the
basis of a 360-day year of twelve 30-day months.

     (c)   No dividends may be declared or paid or funds set apart for the
payment of dividends on any Parity Stock for any period unless full cumulative
dividends shall have been or contemporaneously are declared and paid in full or
declared and a sum in cash or shares of Common Stock sufficient for such payment
set apart for such payment on the Series G1 Preferred Stock. If full dividends
are not so paid, the Series G1 Preferred Stock shall share dividends pro rata
with the Parity Stock. No dividends may be paid or set apart for such payment on
Junior Stock (except dividends on Junior Stock payable in additional shares of
Junior Stock) and no Junior Stock or Parity Stock may be repurchased or
otherwise retired for value nor may funds be set apart for payment with respect
thereto, if cumulative dividends have not been paid in full on the Series G1
Preferred Stock in cash or shares of Common Stock; provided, however, that the
Corporation may repurchase Junior Stock (i) in the open market from time to time
as and to the fullest extent permitted by Rule l0b-18 promulgated under the
Securities Exchange Act of 1934, as amended (240 C.F.R ss. 10b-18), or
corresponding rule from time to time in effect, and (ii) in a private purchase
or in an "issuer tender offer" as defined in Rule 13e-4 under the Exchange Act
from time to time so long as such repurchases do not exceed ten percent (10%) of
the then outstanding shares of Junior Stock. Dividends on account of arrears for
any past dividend period may be declared and paid at any time without reference
to any regular Dividend Payment Date, to holders of record on a date not more
than forty-five (45) calendar days prior to the payment thereof, as may be fixed
by the Board of Directors of the Corporation. No interest shall be payable with
respect to any dividend payment that may be in arrears. Except as provided
above, so long as any shares of the Series G1 Preferred Stock are outstanding,
the Corporation shall not make payment on account of the purchase or other
retirement of any Parity Stock or Junior Stock, and shall not permit any
corporation or other entity directly or indirectly controlled by the Corporation
to purchase any Parity Stock, Junior Stock or any warrants, rights, calls or
options unless full cumulative dividends determined to be in accordance herewith
on the Series G1 Preferred Stock have been paid (or are deemed paid) in full.

     (d)   All dividends payable on the Series G1 Preferred Stock shall be paid
net of withholding tax, if any, under all applicable laws (including applicable
income tax treaties). The Corporation will, subject to certain exceptions and
limitations set forth below, pay, as additional dividends, such additional
amounts (the "Additional Amounts") to the holder of any Series G1 Preferred
Stock as may be necessary in order that every net payment of the principal or
dividends on such Series G1 Preferred Stock, after withholding for or on account
of any present or future tax, duty, assessment or governmental charge imposed or
levied upon or as a result of such payment by or on behalf of the United States
(or any political subdivision, authority or agency thereof or therein having the
power to tax) (collectively, "Taxes"), will not be less than the amount such
holder would have received if such Taxes had not been withheld, provided that no
Additional Amounts will be payable with respect to a payment which is subject to
such Taxes by reason of such holder being connected with the United States (or
any political subdivision thereof) otherwise than by the mere holding of the
Series G1 Preferred Stock or the receipt of payments made under or with respect
to the Series G1 Preferred Stock. In addition, the

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Corporation will indemnify and hold harmless each holder of the Series G1
Preferred Stock (subject to the exclusion set forth above) and will, upon
written request of each holder (subject to the exclusion set forth above), and
provide that reasonable supporting documentation is provided, reimburse each
other holder for the amount of any Taxes levied or imposed by the United States
and paid by or on behalf of the holder as a result of payments made under or
with respect to the Series G1 Preferred Stock. Any payment made pursuant to this
paragraph shall be considered and Additional Amount. If the Corporation becomes
generally subject at any time to any taxing jurisdiction other than or in
addition to the United States, references in this Certificate of Designations to
the United States shall be read and construed as reference to the United States
and/or such other jurisdiction.

     Section 5. Preference on Liquidation.

     (a)     Upon any voluntary or involuntary liquidation, dissolution or
winding-up of the Corporation, holders of Series G1 Preferred Stock shall be
entitled to be paid, out of the assets of the Corporation available for
distribution to stockholders, the liquidation preference of $100.00 per share of
Series G1 Preferred Stock, plus, without duplication, an amount in cash equal to
all accrued and unpaid dividends thereon to the date fixed for liquidation,
dissolution or winding-up (including an amount equal to a prorated dividend for
the period from the last Dividend Payment Date, or if such event is prior to the
first Dividend Payment Date, from the Closing Date, to the date fixed for
liquidation, dissolution or winding-up), before any distribution is made on any
Junior Stock, including, without limitation, any class of common stock of the
Corporation.

     (b)     If, upon any voluntary or involuntary liquidation, dissolution or
winding-up of the Corporation, the amounts payable with respect to the Series G1
Preferred Stock and all Parity Stock are not paid in full, then the assets of
the Corporation available for distribution among the holders of the Series G1
Preferred Stock and any Parity Stock shall bear to each other the same ratio
that the full amounts payable on liquidation, dissolution or winding-up of the
Corporation to the holders of shares of Series G1 Preferred Stock and any Parity
Stock bear to each other.

     (c)     After payment of the full amount of the liquidation preference and
accumulated and unpaid dividends to which they are entitled, the holders of
shares of Series G1 Preferred Stock shall not be entitled to any further
participation in any distribution of assets of the Corporation.

     (d)     Neither the sale, conveyance, exchange or transfer (for cash,
shares of stock, securities or other consolidation) of all or substantially all
of the property or assets of the Corporation nor the consolidation or merger of
the Corporation with one or more entities shall be deemed to be or constitute a
liquidation, dissolution or winding-up of the Corporation.

     (e)     Notice of any payment to the holders of Series G1 Preferred Stock
as a result of the liquidation, dissolution or winding-up of the Corporation,
stating the payment date or dates when and the place or places where the amounts
distributable in such circumstances shall be payable, shall be given not more
than sixty (60) but not less than thirty (30) days prior to any payment date
stated therein, to the holders of shares of Series G1 Preferred Stock as
provided in Section 11 herein.

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     Section 6.   Voting. The holders of Series G1 Preferred Stock shall have no
voting rights except as required by law. In exercising any voting rights, each
outstanding share of Series G1 Preferred Stock shall be entitled to one vote.

     Section 7.   Holder Conversion Rights.

     (a)     Each holder of shares of Series G1 Preferred Stock shall have the
right ("Conversion Right"), subject as provided herein and to any applicable
laws and regulations, at any time and from time to time at the holder's option
to convert each share of Series G1 Preferred Stock into shares of Common Stock
at the conversion price (subject to adjustment as described in Section 8 below)
of $1.25 per share of underlying Common Stock (the "Conversion Price") for each
$100.00 liquidation value per share of Series G1 Preferred Stock plus the amount
of any accrued and unpaid dividends (whether or not earned or declared) on the
Series G1 Preferred Stock delivered for conversion as specified herein
(including an amount equal to a prorated dividend from the immediately preceding
Dividend Payment Date to the date of such conversion, or, if such conversion is
prior to the first Dividend Payment Date, from the Closing Date to the date of
such conversion); provided, however, that the Corporation may, at its sole
discretion, pay any or all of such accrued and unpaid dividends in cash. Subject
to the provisions of the DGCL, no fractional shares of Common Stock shall be
issued upon conversions but, the number of shares shall be rounded up or down to
the nearest whole number.

     (b)     If the Corporation elects to pay any accrued and unpaid dividends
in cash, the amount of any such accrued and unpaid dividends shall be promptly
sent to the holder thereof by means of check or other means provided by the
Corporation after the receipt of the notice and funds, if any, referred to in
Sections 7(d) and 7(e) below.

     (c)     As promptly as practicable after the surrender of certificates for
shares of the Series G1 Preferred Stock for conversion and the receipt of the
notice and funds, if any, as described in Sections 7(d) and 7(e) below, the
Corporation shall issue and shall deliver to such holder, or on such holder's
written order, a certificate or certificates for the number of shares of Common
Stock issuable upon the conversion of such shares of the Series G1 Preferred
Stock in accordance with the provisions of this Section 7, together with
certificates representing the number of shares of Common Stock in payment of any
accrued but unpaid dividends if the Corporation elects to pay such dividends in
Common Stock. Each conversion with respect to such shares of the Series G1
Preferred Stock shall be deemed to have been effected immediately prior to the
close of business on the date on which the certificates for shares of the Series
G1 Preferred Stock shall have been surrendered and such notice shall have been
received by the Corporation as aforesaid, and the Person or Persons entitled to
receive the Common Stock issuable upon such conversion shall be deemed for all
purposes to be the record holder or holders of such Common Stock upon that date.

     (d)     In order to exercise the conversion right, the holder of each share
of Series G1 Preferred Stock to be converted shall surrender that certificate
representing such shares, duly endorsed or assigned to the Corporation or in
blank, at the office of the transfer agent for the Series G1 Preferred Stock and
shall give written notice to the Corporation in the form of

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Exhibit A attached hereto. Such notice shall also state the name or names (with
address) in which the shares of Common Stock which shall be issuable upon such
conversion shall be issued. Each share surrendered for conversion shall, unless
the shares issuable on conversion are to be issued in the same name as the name
in which such shares of the Series G1 Preferred Stock is registered, be duly
endorsed by, or accompanied by, instruments of transfer (in each case, in form
reasonably satisfactory to the Corporation), duly executed by the holder or such
holder's duly authorized attorney-in-fact.

     (e)     If a holder converts shares of the Series G1 Preferred Stock, the
Corporation shall pay any and all documentary, stamp or similar issue or
transfer tax payable in respect of the issue or delivery of the shares of the
Series G1 Preferred Stock (or any other Securities issued on account thereof
pursuant hereto) or Common Stock upon the conversion; provided, however, the
Corporation shall not be required to pay any such tax that may be payable
because any such shares are issued at the request of the holder in a name other
than the name of the holder. In the event that the shares are to be issued in a
name other than that of the holder, the holder shall provide funds necessary to
pay any and all of the foregoing taxes, if any shall be applicable.

     (f)     The Corporation shall reserve out of its authorized but unissued
Common Stock or its Common Stock held in treasury enough shares of Common Stock
to permit the conversion of all of the outstanding shares of the Series G1
Preferred Stock, but in no event shall the Corporation be required to reserve
sufficient shares of Common Stock to permit the conversion of any accrued and
unpaid dividends on the Series G1 Preferred Stock. The Corporation shall from
time to time, in accordance with the DGCL, increase the authorized amount of its
Common Stock if at any time the authorized amount of its Common Stock remaining
unissued shall not be sufficient to permit the conversion of all shares of the
Series G1 Preferred Stock at the time outstanding. If any shares of Common Stock
required to be reserved for issuance upon conversion of shares of the Series G1
Preferred Stock hereunder require registration with or approval of any
governmental authority under any federal or state law before the shares may be
issued upon conversion, the Corporation shall in good faith and as expeditiously
as possible endeavor to cause the shares to be so registered or approved. All
shares of Common Stock delivered upon conversion of the shares of the Series G1
Preferred Stock will, upon delivery, be duly authorized and validly issued,
fully paid and nonassessable, free from all taxes, liens and charges with
respect to the issue thereof.

     Section 8.   Conversion Price Adjustments.

     (a)     Subdivision of Common Stock. In case outstanding shares of Common
Stock shall be subdivided into a greater number of shares of Common Stock, the
Conversion Price in effect at the opening of business on the day following the
day upon which such subdivision becomes effective shall be proportionately
reduced, and, conversely, in case outstanding shares of Common Stock shall each
be combined into a smaller number of shares of Common Stock, the Conversion
Price in effect at the opening of business on the day following the day upon
which such combination becomes effective shall be proportionately increased,
such reduction or increase, as the case may be, to become effective immediately
after the opening of business on the day following the day upon which such
subdivision or combination becomes effective.

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     (b)     Certificate of Adjustment and Notice. Whenever the Conversion Price
is adjusted as herein provided, the Corporation shall promptly file with the
transfer agent for the Series G1 Preferred Stock a certificate of an officer of
the Corporation setting forth the Conversion Price after the adjustment and
setting forth a brief statement of the facts requiring such adjustment and a
computation thereof. The Corporation shall promptly cause a notice of the
adjusted Conversion Price be given to the holders of shares of the Series G1
Preferred Stock as provided in Section 11 herein.

     (c)     Adjustment in Conversion Price in Case of Certain Events. In case
the Corporation shall take any action affecting the Common Stock, other than
actions described in Section 7 or this Section 8, which in the opinion of the
Board of Directors would materially adversely affect the conversion right of the
holders of the shares of the Series G1 Preferred Stock, the Conversion Price may
be adjusted, to the extent permitted by law, in such manner, if any, and at such
time, as the Board of Directors may determine to be equitable in the
circumstances; provided, however, that in no event shall the Board of Directors
be required to take any such action.

     (d)     Registration of Conversion Shares. The Corporation shall file a
registration statement on Form S-3 (or such other form as the Corporation may
determine is appropriate) with respect to the Conversion Shares at the earliest
practicable date, but in any event prior to 90 days following the receipt by the
Company of the first notice of conversion from a holder of Series G1 Preferred
Stock in respect of all the Common Stock that may be issuable at any time upon
the conversion of any of the Series G1 Preferred Stock ("Conversion Shares").
The Corporation shall use its best efforts to cause the Commission to declare
such registration statement (and any necessary amendments thereto) effective.
The Corporation shall also use its best efforts to maintain the effectiveness of
such registration statement, and to refile such a registration statement from
time to time in the event its effectiveness lapses, until all Conversion Shares
either issued or that may be issued are Freely Tradeable (as defined in Section
13 below) in the United States.

     Section 9.   Mandatory Conversion by Corporation.

     (a)     At any time after the earlier of (i) the registration statement
referred to in subsection (d) above has been declared effective, or (ii) the
Conversion Shares are Freely Tradeable, the Corporation may, at its option,
cause all of the outstanding Series G Preferred Stock to be converted into
shares of Common Stock, in accordance with Section 9(b), at any time and from
time to time, if the average of the Market Prices of the Common Stock over the
Stock Exchange Business Days in any twenty (20) consecutive calendar day period
ending not more than five (5) days prior to the giving of the notice referred to
below equaled or exceeded the Target Price (as defined below).

     The "Target Price" shall initially equal the Conversion Price multiplied by
110%. On the first day following the first anniversary of the Closing Date, the
Target Price shall be reduced to an amount equal to (x) the Conversion Price
less $0.10 (the "Adjusted Conversion Price") multiplied by (y) 110%. On the
first day following each anniversary of the Closing Date thereafter, the Target
Price shall be reduced to an amount equal to (x) the Adjusted Conversion

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Price then in effect less $0.10 multiplied by (y) 110%. Notwithstanding the
preceding, (i) if the outstanding shares of Common Stock shall be subdivided
into a greater number of shares of Common Stock, such $0.10 amount described in
the preceding two sentences shall be proportionately reduced on the day upon
which such subdivision becomes effective, and (ii) if the outstanding shares of
Common Stock shall be combined into a smaller number of shares of Common Stock,
such $0.10 amount described in the preceding two sentences shall be
proportionately increased on the day such combination becomes effective. In case
the Corporation shall take any action affecting the Common Stock, other than the
aforementioned adjustments, which in the Board of Directors would materially
adversely affect the conversion right of the holders of the shares of Series G
Preferred Stock, such $1.25 valuation may be adjusted, to the extent permitted
by law, in such manner, if any, and at such time, as the Board of Directors may
determine to be equitable in the circumstances; provided, however, that in no
event shall the Board of Directors be required to take such action. In no event
shall the Target Price be less than $0.81; provided, however, that (A) if the
outstanding shares of Common Stock shall be subdivided into a greater number of
shares of Common Stock, such $0.81 amount shall be proportionately reduced on
the day upon which such subdivision becomes effective, and (ii) if the
outstanding shares of Common Stock shall be combined into a smaller number of
shares of Common Stock, such $0.81 amount shall be proportionately increased on
the day such combination becomes effective. By way of example only, the initial
Target Price shall be $1.375 (or $1.25 - $0 x 110%), and on the first day
following the first anniversary of the Closing Date, the Target Price shall be
$1.265 (or ($1.25 - $0.10) x 110%), and on the first day following the second
anniversary of the Closing Date, the Target Price shall be $1.155 (or ($1.15 -
$0.10) x 110%).

     (b)     Each share of Series G1 Preferred Stock shall be converted into a
number of shares of Common Stock equal to: (x) each $100.00 liquidation value
per share of Series G1 Preferred Stock plus the amount of any accrued and unpaid
dividends (whether or not earned or declared) on the Series G1 Preferred Stock
(including an amount equal to a prorated dividend from the immediately preceding
Dividend Payment Date, or if such conversion is prior to the first Dividend
Payment Date, from the Closing Date, to the date of such conversion) divided by
(y) the Conversion Price.

     Notwithstanding the preceding, the Corporation may, at its sole discretion,
pay any or all of the accrued and unpaid dividends in cash. Subject to the
provisions of the DGCL, no fractional shares of Common Stock shall be issued the
optional conversion but, the number of shares shall be rounded up or down to the
nearest whole number. The amount of any accrued and unpaid dividends that the
Corporation elects to pay in cash shall be promptly sent to the holder thereof
by means of check or other means provided by the Corporation.

     (c)     The Corporation shall give thirty (30) days notice as provided in
Section 11 hereof of its intent to convert in accordance with this Section 9 no
later than thirty (30) calendar days from the end of the twenty (20) day period
described above. Upon the giving of the notice referred to above, the
Corporation shall be bound to convert the Series G1 Preferred Stock as to which
notice has been provided. During the 30 day notice period, holders of the Series
G1 Preferred Stock will retain their right to convert their shares of Series G1
Preferred Stock in accordance with Section 7 above.

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     Section 10. Optional Redemption by Corporation.

     (a)  Optional Redemption. In addition to its right to redeem the Series G1
Preferred Stock as provided in Section 9 above, the Corporation shall have the
option to redeem the Series G1 Preferred Stock in whole or in part in cash at
any time, and from time to time, unless the holder thereof shall have converted
such stock into Common Stock pursuant to Section 7 prior to the date of
redemption hereof, at a redemption price ("Redemption Price") equal to (i)
$100.00 per share and (ii) accrued and unpaid dividends (whether or not
declared), such dividends being payable in cash or Freely Tradeable Common Stock
(including an amount equal to a prorated dividend from the immediately preceding
Dividend Payment Date, or if such conversion is prior to the first Dividend
Payment Date, from the Closing Date, to the redemption date).

     (b)  Procedures for Redemption.

          (i)   In case of redemption of less than all shares of Series G1
     Preferred Stock at the time outstanding, the shares to be redeemed shall be
     selected pro rata, at random, or by lot or a method that complies with the
     requirements of any national stock exchange on which Series G1 Preferred
     Stock is listed as determined by the Board of Directors in its sole
     discretion.

          (ii)  Notice of any redemption shall be given as provided in Section
     11 by or on behalf of the Corporation not more less than thirty (30) days
     prior to the date of redemption hereof; provided, however, that such notice
     of redemption may be a conditional notice of redemption which may condition
     the redemption upon making the redemption subject to the prior conversion
     of the Series G1 Preferred Stock before the redemption date; and provided
     further, that no failure to give such notice or any defect therein or in
     the transmission or mailing thereof shall affect the validity of the
     proceedings for the redemption of any shares of Series G1 Preferred Stock
     except as to the holder to whom the Corporation has failed to give notice
     or except as to the holder to whom notice was defective. In addition to any
     information required by law, such notice shall state: such redemption is
     being made pursuant to the optional redemption provisions hereof, the date
     of redemption; the Redemption Price; the number of shares of Series G1
     Preferred Stock to be redeemed and, if less than all shares held by such
     holder are to be redeemed; the number of such shares to be redeemed; the
     place or places where certificates for such issued shares are to be
     surrendered for payment of the Redemption Price; and that dividends on the
     shares to be redeemed shall cease to accrue on the date of redemption. Upon
     the expiry of the notice so given, except with respect to the conditions
     specified above, the Corporation shall become obligated to redeem at the
     time of redemption specified thereon all shares called for redemption.

          (iii) If notice has been given in accordance with Section 10(b)(ii)
     above and provided that on or before the date of redemption specified in
     such notice, all funds necessary for such redemption shall have been set
     aside by the Corporation, separate and apart from its other funds in trust
     for the pro rata benefit of the holders of the shares so called for
     redemption, so as to be, and to continue to be available therefor, then,
     from and

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     after the date of redemption, dividends on the shares of the Series G1
     Preferred Stock so called for redemption shall cease to accrue, and said
     shares shall no longer be deemed to be outstanding and shall not have the
     status of shares of Series G1 Preferred Stock, and all rights of the
     holders thereof as shareholders of the Corporation (except the right to
     receive from the Corporation the Redemption Price) shall cease. Upon
     surrender, in accordance with said notice, of the certificates for any
     issued shares so redeemed (properly endorsed or assigned for transfer, if
     the Corporation shall so require and the notice shall so state), such
     shares shall be redeemed by the Corporation at the Redemption Price by
     mailing a check to such holder's last registered address listed on the
     stock transfer records of the Corporation, or as otherwise agreed by the
     holders of Series G1 Preferred Stock and the Corporation. In case fewer
     than all the shares represented by any such certificate are redeemed, a new
     certificate or certificates shall be issued representing the unredeemed
     shares without cost to the holder thereof.

          (iv)  Any funds deposited with a bank or trust corporation for the
     purpose of redeeming Series G1 Preferred Stock shall be irrevocable except
     that: the Corporation shall be entitled to receive from such bank or trust
     company the interest or other earnings, if any, earned on any money so
     deposited in trust, and the holders of any shares redeemed shall have no
     claim to such interest or other earnings; and any balance of monies so
     deposited by the Corporation and unclaimed by the holders of the Series G1
     Preferred Stock entitled thereto at the expiration of two years from the
     applicable date of redemption shall be repaid, together with any interest
     or other earnings earned thereon, to the Corporation, and after any such
     repayment, the holders of the shares entitled to the funds so repaid to the
     Corporation shall look only to the Corporation for payment without interest
     or other earnings.

          (v)   No Series G1 Preferred Stock may be redeemed except with funds
     legally available for the payment of the Redemption Price.

          (vi)  Holders of Series G1 Preferred Stock shall retain the conversion
     rights described in Section 7 hereof until the date of any redemption of
     the shares of Series G1 Preferred Stock in accordance with this Section 10.

     (c)  Redemption by Conversion. In addition to the rights of conversion
pursuant to Section 9 hereof, on or after June 1, 2004, the Corporation may
further elect, in any six (6) month period, to redeem up to 50% of the
outstanding Series G1 Preferred Stock in accordance with this Section 10(c) by
requiring their redemption on thirty (30) days notice pursuant to the terms of
this Section 10(c) (the "Redemption by Conversion Option"). The redemption price
for purposes of this Section 10(c) shall be equal to the average Market Price of
the Common Stock during the twenty (20) consecutive Stock Exchange Business Days
ending not more than five (5) Stock Exchange Business days prior to the date
notice is given by the Corporation concerning its exercise of this Redemption by
Conversion Option, subject to appropriate adjustments to account for the effects
of dividends, distributions, stock splits, recapitalizations and similar events.
If the Market Capitalization of the Corporation is less than $300 million on the
date the notice by the Corporation of its exercise of this Redemption by
Conversion Option is given, then each share of Series G1 Preferred Stock will be
redeemed for the number of shares of

                                       10

<PAGE>

Common Stock equal to 110% of the $100.00 liquidation value per share (the
"Redemption Value") divided by the redemption price. If the Market
Capitalization of the Corporation is $300 million or more on the date the notice
by the Corporation of its exercise of this Redemption by Conversion Option is
given, then each share of Series G1 Preferred Stock will be redeemed for the
number of shares of Common Stock equal to 105% of the Redemption Value divided
by the redemption price. The amount of the accrued and unpaid dividends (whether
or not earned or declared) accrued by the Series G1 Preferred Stock delivered
for redemption as specified above (computed to the end of the day the Series G1
Preferred Stock is so redeemed) shall be sent to the holder thereof by means of
check or other means established by the Corporation, if the dividend is in cash,
or if the dividend is in shares of Common Stock, each as determined by the
Corporation, by such means as selected by the Corporation.

     Section 11. Notice. Where this Certificate of Designations provides for
notice of any event to the holders of the Series G1 Preferred Stock by the
Corporation or any other Person, such notice shall be sufficiently given (unless
otherwise herein specifically provided) if published in the Authorized
Newspapers.

     Section 12. General Provisions Relating to the Series G1 Preferred Stock.

     (a)  Form. The Series G1 Preferred Stock shall be issued in fully
registered form in the form satisfactory to the Corporation.

     (b)  Compliance with United States Securities Laws. Nothing contained
herein shall be deemed to authorize any transfers of certificates of the Series
G1 Preferred Stock otherwise than accordance with the Securities Act. Neither
the Corporation or its transfer agent shall recognize or give effect to any
attempt to transfer (by book entry or otherwise) or convert any Series G1
Preferred Stock or any interest therein in violation of either the Securities
Act. The certificates representing the Series G1 Preferred Stock and the
Conversion shares shall bear restrictive legends thereon recommend by legal
counsel for the Corporation regarding the restrictions on the transferability
thereof to ensure compliance the Securities Act until the Series G1 Preferred
Stock and/or the Conversion shares, as the case may be become Freely Tradeable.

     Section 13. Certain Definitions.

     "Alternative Stock Exchange" means any other national or regional stock
exchange or quotation service such as the Nasdaq Market System or any similar
quotation service maintained by the National Quotation Bureau or any successor
thereto.

     "Authorized Newspapers" means the Luxembourg Wort of Luxembourg and The
Financial Times (European Edition) of London, England. If either such newspaper
shall cease to be published, the Corporation shall substitute for it another
newspaper in Europe, customarily published at least once a day for at least five
(5) days in each calendar week, of general circulation. If, because of temporary
suspension of publication or general circulation of either such newspaper or for
any other reason, it is impossible or, in the opinion of the Corporation,
impracticable to make any publication of any notice required by this Certificate
of Designations in the manner herein provided, such publication or other notice
in lieu thereof which is made by

                                       11

<PAGE>

the Corporation in the exercise of its reasonable discretion shall constitute a
sufficient publication of such notice.

     "Capital Stock" of any Person means the Common Stock or preferred stock of
such Person. Unless otherwise stated herein or the context otherwise requires,
"Capital Stock" means Capital Stock of the Corporation.

     "Closing Date" means the date of which the Series G1 Preferred Stock is
sold to the holders thereof.

     "Commission" means the Securities and Exchange Commission.

     "Common Stock Valuation Method" has the meaning given to it in Section 4(a)
hereof.

     "Conversion Agent" means any Person (including the Corporation acting as
Conversion Agent) authorized by the Corporation to effect conversions of the
Series G1 Preferred Stock on behalf of the Corporation.

     "Dividend Payment Date" has the meaning given to it in Section 4(b) hereof.

     "Freely Tradeable" means, with respect to the Common Stock issuable upon
the conversion of or the payment of a dividend upon the Series G1 Preferred
Stock, that under the Securities Act the holders thereof may then offer and sell
any amount of such outstanding securities to the public in the United States in
transactions that are not brokers' transactions (as defined in the Securities
Act) either (i) pursuant to an effective registration statement then in effect
or (ii) pursuant to Rule 144(k). For purposes of determining whether such
securities are Freely Tradeable, it shall be assumed that no affiliate of the
issuer has ever held such securities from and after their issuance.

     "Group" means the Corporation and all its Principal Subsidiaries.

     "Market Capitalization" means, on any date, the average, over the thirty
(30) calendar day period commencing thirty-five (35) calendar days prior to such
date, of the product of the Market Price of the Common Stock and the number of
shares of Common Stock of the Corporation issued and outstanding on such date;
provided, however, that appropriate adjustments shall be made to the Market
Prices and number of shares used in determining such Market Capitalization to
account fairly for the effect of dividends payable in equity securities of the
Corporation or any other Person, spin-offs of subsidiaries, mergers in which the
Corporation or a Principal Subsidiary is a constituent party, and similar
events.

     "Market Price" means the closing sales price on the American Stock Exchange
or any Alternative Stock Exchange on any Stock Exchange Business Day.

     "Person" means any individual, corporation, partnership, association, trust
or other entity or organization, including a government or political subdivision
or any agency or instrumentality thereof.

                                       12

<PAGE>

     "Principal Subsidiary" means a Subsidiary of either the Corporation or any
Principal Subsidiary:

     (a)  whose gross assets represent 10 percent or more of the consolidated
gross assets of the Group as calculated by reference to the then latest audited
financial statements of the Group; or

     (b)  to which is transferred all or substantially all of the business,
undertaking and assets of a Subsidiary of the Corporation which immediately
prior to such transfer is a Principal Subsidiary, whereupon the transferor
Subsidiary shall immediately cease to be a Principal Subsidiary and the
transferee Subsidiary shall cease to be a Principal Subsidiary under the
provisions of this sub-paragraph (b) (but without prejudice to the provisions of
sub-paragraph (a) above), upon publication of its next audited financial
statements.

     "Property" means any kind of property or asset, whether real, personal,
mixed, or tangible or intangible, and any interest therein.

     "Securities Act" means the United States Securities Act of 193 as in effect
on the date of the filing of this Certificate with the Secretary of State of
Delaware or as such act may hereafter be amended.

     "Series G1 Preferred Stock" means the Corporation's Series G1 Convertible
Preferred Stock, $1.00 par value.

     "Stock Exchange Business Day" means as any day (other than a Saturday or
Sunday) on which the American Stock Exchange or the Alternative Stock Exchange,
as the case may be, is open for business.

     "Subsidiary" of any Person means any Corporation of which at least a
majority of the shares of stock having by the terms thereof ordinary voting
power to elect a majority of the Board of Directors of such Corporation
(irrespective of whether or not at the time stock of any other class or classes
of such Corporation shall have voting power by reason of the happening of any
contingency) is directly or indirectly owned or controlled by any one of or any
combinations of the Corporation or one or more of its Subsidiaries."

                                      *****

                                       13

<PAGE>

     IN WITNESS WHEREOF, the Corporation has caused this Certificate to be duly
executed on its behalf by its undersigned Assistant Secretary this 19/th/ day of
October, 2000.

                                              HARKEN ENERGY CORPORATION,
                                              a Delaware corporation


                                              By:   /s/ Karen Kerr-Johnson
                                                 -------------------------------
                                              Name:  Karen Kerr-Johnson
                                              Title: Assistant Secretary

                                       14

<PAGE>

                                    EXHIBIT A

                              NOTICE OF CONVERSION

To:   Harken Energy Corporation

To:   [Conversion Agent]

     The undersigned holder of the Series G1 Convertible Preferred Stock, par
value U.S. $1.00 (the "Preferred Stock") of Harken Energy Corporation (the
"Corporation") in the aggregate liquidation preference value of U.S. $100.00
irrevocably exercises the option to convert [insert number] shares of Preferred
Stock into shares of Common Stock of the Corporation, par value U.S. $0.01 (the
"Common Stock"), in accordance with the terms of the Certificate of Designations
relating to the issuance by the Corporation of the Preferred Stock and directs
that the Common Stock issuable and deliverable upon such conversion be issued
and delivered to the undersigned in the name and at the address set forth below.

     If the Common Stock is not Freely Tradeable at the date hereof, the
undersigned holder hereby certifies to the Corporation that it:

     (1) (a) is an "accredited investor" (as defined in Rule 501 of Regulation D
under the U.S. Securities Act of 1933, as amended (the "Securities Act")), or
(b) is acquiring the Common Stock in a transaction exempt from the registration
requirements of the Securities Act; and

     (2) acknowledges that the Common Stock has not been registered under the
Securities Act and are "restricted securities" within the meaning of the
Securities Act; and

     (3) understands and agrees that if within two years after the date of the
original issuance of the Preferred Stock or within three months after it ceases
to be an affiliate (within the meaning of Rule 144 under the Securities Act) of
the Corporation, upon conversion thereof the Common Stock may be resold,
pledged, or transferred only (i) to the Corporation, (ii) pursuant to an
exemption from the registration requirements of the Securities Act provided by
Rule 144 (if applicable) under the Securities Act, or (iii) pursuant to an
effective registration statement under the Securities Act, in each case in
accordance with any applicable securities law of any state of the United States;
and

     (4) it understands that the certificates representing the Common Stock will
bear a restrictive legend describing the foregoing restriction on transfer,
unless otherwise agreed by the Corporation.

     If the Common Stock is to be issued in the name of a person other than the
undersigned or a nominee of the undersigned, the undersigned will pay all
transfer taxes payable with respect thereto and is delivering herewith a
certificate in proper form that the applicable restrictions on transfer have
been complied with.

<PAGE>

     All terms not otherwise defined herein shall have the respective meanings
set forth in the Certificate of Designations relating to the Preferred Stock.

                                     * * * *

DATE:

                                               Name of Holder


                                               Signature(s) of Holder

Address for Delivery of Shares:


Name for Registration of Shares (if different than Holder):