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                                                                     EXHIBIT 10h



                             ROWAN COMPANIES, INC.
                   1986 CONVERTIBLE DEBENTURE INCENTIVE PLAN
                                   AS AMENDED

     1.       Purpose.  The Rowan Companies, Inc. 1986 Convertible Debenture
Incentive Plan (the "Plan") is intended to promote the interests of Rowan
Companies, Inc. (the "Company") and its stockholders by allowing officers and
other key personnel of the Company and its subsidiaries the opportunity to
invest in corporate debt in the form of the Company's floating interest rate
subordinated debentures (the "Debentures") which are convertible into shares of
Preferred stock, $1 par value, of the Company (the "Preferred Stock"), which
shares of Preferred Stock are convertible into shares of common stock, $.125
par value, of the Company (the "Common Stock"), thereby giving key personnel
added incentive to work toward the continued growth and success of the Company.
The Company's Board of Directors also contemplates that the Plan will enable
the Company and its subsidiaries to compete more effectively for the services
of management personnel needed for the continued growth and success of the
Company.

     2.       Issuance of the Debentures.  The Company shall have authority to
issue Debentures in such amounts and to such of the key employees of the
Company and its subsidiaries (as defined by Section 425 of the Internal Revenue
Code of 1954, as amended) as the Committee (as defined in Section 9) shall from
time to time determine. Such employees purchasing Debentures are designated
herein as "Purchasers".

     3.       General Terms and Conditions of the Debentures.

     Section 3.01.  General.  The Committee shall from time to time determine
with respect to each series of Debentures to be issued the interest rate
thereof, the conversion price applicable thereto (including the conversion
ratio of the Preferred Stock), and such other terms and conditions of the
Debentures, all to the extent not inconsistent with the provisions of this
Plan.

     Section 3.02.  Form and Term of Debentures.  Debentures will be issued in
series the terms and conditions of which may differ among series and shall be
in such form and in such denominations as the Committee may approve. Each
series will be due not earlier than five years, or later than ten years, from
the date of issuance, or on such earlier date as the Company redeems any
Debenture, which date is referred to herein as the "Due Date".

     Section 3.03.  Conversion of the Debentures.  Subject to the provisions of
this Section 3.03, the Debentures will be convertible at the conversion price
in effect at the time of conversion into fully paid and non-assessable shares
of Preferred Stock, which will be immediately convertible into fully paid and
nonassessable shares of Common Stock of the Company, at any time in quantities
and after time periods determined by the Committee, which in no event will be
less than one year after the date of issuance until the close of business on
the Due Date. Each series of Debentures shall be convertible into a separate
series of Preferred Stock. The conversion privilege with respect to any
Debenture may be exercised only by the Purchaser thereof or by the estate of a
deceased Purchaser or a beneficiary under such estate.
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         Upon termination of a Purchaser's employment, the conversion privilege
will terminate with respect to each Debenture issued to such Purchaser on the
earlier of the Due Date or a date determined as follows:

                 (a)      Three years after the date of termination of
         employment as a result of retirement or disability;

                 (b)      Two years after the date of termination of employment
         as a result of death;

                 (c)      Prior to the date of termination of employment as a
         result of discharge for cause (as determined in the sole discretion of
         the Committee); or

                 (d)      Three months after the date of termination of
         employment for any other reason.

         The conversion privilege with respect to any Debenture (i) will
terminate if the Purchaser, without the Company's consent, sells, assigns,
transfers, pledges, hypothecates or otherwise disposes of a Debenture except as
permitted by Section 3.04 and (ii) will not be exercisable during such time as
the Debenture is pledged to secure loans as permitted by Section 3.04.

         In no event may any Purchaser or the estate of a deceased Purchaser or
a beneficiary under such estate exercise the conversion privilege associated
with a Debenture prior to one year from the date of issuance of such Debenture
or after the Due Date.

         Notwithstanding the foregoing or any provision in the Plan to the
contrary, effective with the occurrence of a Corporate Change, as defined in
the Company's 1988 Nonqualified Stock Option Plan, each Debenture that has been
issued and outstanding for more than one year as of the date of the Corporate
Change shall automatically be fully convertible on and after the date of such
Corporate Change.

     Section 3.04.  Transfer and Pledge of Debentures.  A Purchaser may not
sell, assign, transfer, pledge, hypothecate or otherwise dispose of a Debenture
except by (i) will or the laws of descent and distribution or (ii) a pledge
("Permitted Pledge") of Debentures to a lender (which may be the Company if a
loan is made pursuant to Section 8 hereof) as security for loans to provide all
or part of the financing to purchase the Debentures. If such loan shall be made
by other than the Company, the Purchaser shall give advance written notice to
the Company prior to making any Permitted Pledge and the Purchaser and such
Lender shall give notice of discharge of any Debenture from a Permitted Pledge,
which notice shall be conclusive evidence that the conversion privilege with
respect to such Debenture will again be exercisable subject to the provisions
of Section 3.03.

     Section 3.05.  Redemption of Debentures.  Subject to the provisions of
this Section 3.05, the Company may, upon at least thirty days prior written
notice to all Debenture holders, redeem as a class, on any interest payment
date, all of the Debentures issued under this Plan. The Company (i) shall
redeem on the next interest payment date after termination of the conversion
privilege with respect thereto any Debenture with respect to which the
conversion privilege has terminated pursuant to clauses (a), (b) or (d) of
Section 3.03, (ii) may redeem any Debenture pledged pursuant to Section 3.04 on
the next interest payment date following notice received by the Company from a
lender (other than the Company) that a loan for which such Debenture is pledged
is in default, provided such default has not been cured, and (iii) may at its
option redeem, on any interest payment date, any Debenture with respect to
which the
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conversion privilege has terminated for any other reason provided in Section
3.03. The holder of any Debenture redeemed pursuant to this Section 3.05 shall
be entitled to receive only the face amount of the Debenture plus accrued
interest thereof to the Due Date.

     4.       Authorized Amount of Debentures. The Company may issue up to
$20,000,000 in aggregate principal amount of all Debentures.

     5.       Effective Date. The Plan shall become effective upon approval
thereof by the vote of the holders of a majority of the shares of Common Stock
of the Company voting at the 1986 Annual Meeting of Stockholders, and shall
expire when all of the Company's obligations with respect to all of the
outstanding Debentures have been discharged; provided, however, that no
Debenture shall be issued after April 1, 1995.

     6.       Offers and Sales Price of Debentures. The Debentures shall be
sold by the Company to Purchasers at a price equal to the higher of (a) face
value plus any accrued interest to the date of sale or (b) the fair market value
of the Debentures as of the date the Purchaser elects to purchase the
Debentures, as determined by an independent investment banking firm. If the
Internal Revenue Service determines that the value of a Debenture at the time
of sale exceeded its sale price and if (a) the Company receives a federal
income tax benefit as a result of such determination and (b) the Purchaser has
contested such determination in a manner which the Company determines to be
appropriate under the circumstances, then the Company will pay to the Purchaser
or his estate or a beneficiary under his estate the lesser of (x) the federal
income tax benefit derived by the Company as a result of the sale of the
Debenture to the Purchaser or (y) the amount estimated by the Company (based on
the highest marginal federal income tax rate applicable with respect to
compensation income for the year in which the sale occurred and the amount
determined by the Internal Revenue Service to be taxable income to the
Purchaser as a result of his purchase of the Debenture) to be Purchaser's
federal income tax liability resulting from his purchase of the Debenture.

         The Debentures may be offered only on April 15, May 30, August 30 and
November 30 of each year (any such date is referred to herein as an "Offering
Date"). An employee may elect to purchase all or none of the Debentures offered
to him on an Offering Date by giving written notice to the Company of his
election within 10 business days of such Offering Date. Payment for such
Debentures shall be in cash or in Common Stock (valued at the reported last
sales price of Common Stock prior to the date of such payment, as shown on the
Composite Tape for securities listed on the New York Stock Exchange) and shall
be made within 20 business days of such Offering Date.

     7.       Conversion Price.  The price (the "Conversion Price") at which
shares of Preferred Stock shall be delivered upon conversion of a series of
Debentures shall be set at a price at least equal to the reported last sales
price of the Company's Common Stock prior to the date of sale of such series of
Debentures, as shown on the Composite Tape for securities listed on the New
York Stock Exchange. The number of shares of Common Stock which shall be
delivered upon conversion of any shares of a series of Preferred Stock (the
"Conversion Ratio") shall not exceed the face value of the related Debentures
which were converted into such Preferred Stock divided by the reported last
sales price of the Company's Common Stock prior to the date of sale of such
Debentures as shown on the composite tape for securities listed on the New York
Stock Exchange. Upon any change in the capital stock of the Company, through
merger, consolidation, reorganization, recapitalization, stock dividend, stock
split, spin-off, split up, dividend in kind or other change in the corporate
structure or distribution to stockholders, appropriate adjustments to the
Conversion Price and Conversion Ratio and the kind of shares delivered upon
conversion of the Debentures and Preferred Stock may be made by the Committee
(or, if the Company is
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not the surviving corporation in any such transaction, the board of directors
of the surviving corporation) with respect to both outstanding and unissued
Debentures and Preferred Stock. If the Internal Revenue Service determines that
the conversion of Debentures into Preferred Stock or that the subsequent
conversion of Preferred Stock into Common Stock is a taxable transaction and if
(a) the Company receives a federal income tax benefit as a result of such
determination and (b) the Purchaser has contested such determination in a
manner which the Company deems to be appropriate under the circumstances, then
the Company will pay to the Purchaser or his estate or a beneficiary under his
estate the lesser of (x) the federal income tax benefit derived by the Company
with respect to such conversion or (y) the amount estimated by the Company
(based on the highest marginal federal income tax rate applicable with respect
to compensation income for the year in which the conversion occurred and the
amount determined by the Internal Revenue Service to be taxable income to the
Purchaser as a result of such conversion) to be Purchaser's federal income tax
liability resulting from such conversion.

     8.       Company Loans.  The Company may, from time to time, make full
recourse (or, in the case of (1) an aggregate of $5,125,000 in principal amount
of loans made by the Company to Purchasers on June 13, 1986 and (2) an
aggregate of $10,300,000 in principal amount of loans made by the Company to
Purchasers on November 30, 1994, non- recourse) loans ("Company Loans") to
Purchasers for the purpose of providing all or part of the financing necessary
to purchase any Debenture; provided, however, that the maximum amount of the
Company Loan shall not exceed the purchase price of the Debentures. Subject to
the foregoing, Company Loans may be made to such Purchasers in such amounts
bearing interest at such rates (not less than the higher of the interest rate
on the Debenture or a floating rate determined under Sections 483 and 1274(d)
of the Internal Revenue Code of 1954, as amended), shall be secured by a pledge
of and lien on the Debenture (which may be inferior to the pledge and lien
securing the Bank Loan) and on such other terms and conditions as the Committee
may from time to time approve.

     9.       Administration.  The Plan shall be administered by a committee of
the Board of Directors (the "Committee") which shall consist of three or more
persons. No Debentures may be sold to any member of the Committee during the
term of his membership on the Committee. No person shall be eligible to serve
on the Committee unless he is a "disinterested person" within the meaning of
Paragraph (d)(3) of Rule 16b-3, under the Securities Exchange Act of 1934 or
any successor thereto as then in effect ("Rule 16b-3"). The members of the
Committee shall be appointed by the Board of Directors, and any vacancy on the
Committee shall be filled by the Board of Directors.

     Subject to the foregoing paragraphs, the Committee shall interpret the
Plan and the Debentures sold under the Plan, shall make such rules as it deems
necessary for the proper administration of the Plan, shall make all other
determinations necessary or advisable for the administration of the Plan and
shall correct any defect or supply any omission or reconcile any inconsistency
in the Plan or in any Debenture in the manner and to the extent the Committee
deems desirable to administer the Plan or the Debentures. The Committee's
determination of any matter within its authority shall be conclusive and
binding upon the Company and all other persons.

     10. Amendment and Discontinuance.  Subject to the provisions of this
Section 10, the Committee may amend, suspend or terminate the Plan. No
amendment, suspension or termination of the Plan may:

                 (a)      Without the consent of the holder of a Debenture,
     terminate his Debenture or adversely affect his rights under the
     Debenture in any material respect;
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                 (b)      Without the consent of a majority of the shares of
     voting stock of the Company voting at any meeting of Stockholders (i)
     increase the amount of Debentures available under the Plan, (ii)
     change materially the persons eligible to purchase Debentures under
     the Plan, (iii) increase materially the benefits under the Plan, or
     (iv) extend the termination date of the Plan; or

                 (c)      Cause the plan to fail to meet the requirements of
     Rule 16b-3.


     11.      Other Provisions.

                 (a)      The Purchaser of a Debenture shall not be entitled to
     any rights as a stockholder of the Company until such Purchaser has
     exercised the conversion privilege contained in the Debenture.

                 (b)      No Debenture shall be construed as limiting any right
     which the Company or any subsidiary of the Company may have to
     terminate at any time, with or without cause, the employment of a
     Purchaser to whom a Debenture has been sold.

                 (c)      Notwithstanding any provision of the Plan or the
     terms of any Debenture sold pursuant to the Plan, (i) the Company
     shall not be required to issue any Debentures hereunder if such
     issuance would, in the judgment of the Committee, constitute a
     violation of any state or Federal law, or of the rules or regulations
     of any governmental regulatory body, and (ii) any amount of interest
     paid or payable on a Debenture which exceeds the amount legally
     payable to a Purchaser under the applicable usury laws will be paid by
     the Company as compensation to the Purchaser.