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                                                                   EXHIBIT 10.26


                         REGISTRATION RIGHTS AGREEMENT

       This REGISTRATION RIGHTS AGREEMENT (the "Agreement") is made and entered
into as of December 10, 1996, by and between Falcon Drilling Company, Inc., a
Delaware corporation (the "Company") and KS Deepsea Drillships, a Norwegian
Limited Partnership ("Drillships").

                              W I T N E S S E T H

       WHEREAS, the Company and Drillships have entered into a Memorandum of
Agreement dated November 6, 1996 (as amended, the "Purchase Agreement")
providing for the sale by Drillships or its guaranteed nominee and the purchase
by the Company or its guaranteed nominee of two Bahamas flag drillships
described therein, a portion of the purchase price of which consists of shares
of the Common Stock of the Company;

       WHEREAS, to induce Drillships to enter into the Purchase Agreement and
as a condition precedent to the Closing thereunder (as such term is defined
therein), the Company has agreed to grant certain registration rights, from
time to time, with respect to the Registrable Securities (as hereinafter
defined) in accordance with the terms and conditions set forth herein.

       NOW, THEREFORE, the parties hereto hereby agree as follows:

       1.     Certain Definitions.  As used in this Agreement, the following
terms shall have the following respective meanings:

       "Agreement" shall have the meaning set forth in the initial paragraph
hereof, and as the same may be amended or modified from time to time in
accordance with the provisions hereof.

       "Closing Date" shall have the meaning set forth in the Purchase
Agreement.

       "Commission" shall mean the Securities and Exchange Commission (or any
successor body thereto).

       "Common Stock" shall mean the common stock, par value $.01 per share, of
the Company which is not registered under the Securities Act, in the amount
specified in the Purchase Agreement.

       "Demand Registration" shall have the meaning set forth in Section 3(a),
hereto

       "Holder" shall have the meaning set forth in Section 4(a).

       "Holder's Counsel" shall have the meaning set forth in Section 6(a)(i).

       "NASD" shall mean the National Association of Securities Dealers, Inc.

       "Person" shall mean any individual, corporation, partnership, limited
liability company, joint venture, association, joint-stock company, trust,
unincorporated organization or government or any agency or political
subdivision thereof.
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       "Purchase Agreement" shall have the meaning set forth in the second
paragraph of this Agreement.

       "Registrable Securities" shall mean the Common Stock of the Company
constituting Registrable Securities as provided in Section 2 of this Agreement.

       "Registration Expenses" shall mean all expenses incident to the
Company's performance of or compliance with the registration rights granted
hereunder, including, without limitation, all registration, filing, listing and
NASD fees, all fees and expenses of complying with securities or blue sky laws,
all word processing, duplicating and printing expenses, messenger and delivery
expenses, the fees and expenses of the Company's independent public
accountants, including fees and expenses associated with any special audits or
"cold comfort" letters required by or incident to such performance and
compliance, and any fees and disbursements of underwriters customarily paid by
issuers and sellers of securities provided, however, that "Registration
Expenses" shall not include fees and expenses of counsel to any holder of
Registrable Securities nor shall it include underwriting discounts, commissions
and transfer taxes, if any.

       "Securities Act" shall mean the Securities Act of 1933, as amended.

       2.     Securities Subject to this Agreement; Representations and
Warranties

       (a)    The securities entitled to the benefit of this Agreement are the
shares of Common Stock of the Company issued to Drillships pursuant to the
Purchase Agreement.  The term "Registrable Securities" shall include the
foregoing securities and shall also include any securities issued as a dividend
or distribution or pursuant to a recapitalization, reorganization,
consolidation or merger on account of Registrable Securities, and includes any
shares of Common Stock received by Drillships by way of sub division of the
outstanding shares of Common Stock into a greater number of shares (by
reclassification, stock split or otherwise).  Certificates representing
Registrable Securities shall contain the following legend on the face thereof:

              The securities represented by this certificate have not been
              registered under the Securities Act of 1933, as amended (the
              "Act"), and may not be offered or sold except pursuant to (i) an
              effective registration statement under the Act, (ii) to the
              extent applicable, Rule 144 under the Act (or any similar rule
              under the Act relating to the disposition of securities), or
              (iii) an opinion of counsel, if such opinion shall be reasonably
              satisfactory to counsel of the Company, that an exemption from
              registration under the Act is available.

The foregoing legend shall remain on the face of such certificates until the
Common Stock represented thereby has been registered with the Commission or
until counsel to the Company has determined that such legend may be removed in
accordance with applicable provisions of the Securities Act and the rules and
regulations promulgated thereunder.

       (b)    A Registrable Security shall cease to be a Registrable Security
when: (i) such security has been effectively registered under the Securities
Act and has been disposed of pursuant to a registration





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statement (which shall not include the sale of Registrable Securities to
Drillships pursuant to the Purchase Agreement); (ii) such security is sold
pursuant to Rule 144 under the Securities Act (or similar provision); (iii)
such security has been otherwise transferred and (A) the Company delivers a new
certificate for such security which does not bear a registration legend and (B)
Holder's counsel is of the reasonable opinion that subsequent disposition of
such security into the public market does not require registration under the
Securities Act; or (iv) such security has ceased to be outstanding.

       (c) The Company represents and warrants, as follow:

       (i)    The Company is a corporation organized, validly existing and in
good standing under the laws of Delaware.

       (ii)   The Company has duly authorized and approved by all requisite
corporate action this Agreement, and the Company has all requisite corporate
power and authority to enter into, execute and deliver this Agreement and
perform its obligations hereunder.

       (iii)  This Agreement has been duly executed and delivered by the
Company and is a valid and binding obligation of it enforceable against it in
accordance with its terms except to the extent that its enforceability may be
subject to applicable bankruptcy, insolvency, reorganization, moratorium and
similar laws affecting the enforcement of creditors' rights generally and
general equitable principals.

       (iv)   The Registrable Securities have been duly and validity authorized
and issued, fully paid and non-assessable and will not subject the Holder
thereof to any liability solely by reason of being such Holder.  The
Registrable Securities are free and clear of all liens, encumbrances,
restrictions and claims of every kind.  The Company has full legal right, power
and authority to sell, assign, transfer and convey the Registrable Securities
so owned and to deliver such Registrable Securities, and the Company can and
will deliver good and marketable title to such Registrable Securities.

       (v) The Company is not subject to any charter, by-law, mortgage, lien,
lease, agreement, instrument, order, law, rule, regulation, judgment or decree,
or any other restriction of any kind or character, which would prevent
consummation of the transactions contemplated by this Agreement.

       (d)    Drillships shall be provided with an opinion of counsel dated the
date hereof, in form and substance reasonably satisfactory to Drillships,
covering the matters set forth in Section 2(c) hereof, and such other matters
as it may reasonably request.

       3.     Demand Registration.

       (a)    At any time on and after March 1, 1997, any Holder or Holders of
50% or more of Registrable Securities may make a written request (specifying
the intended method of disposition) that the Company effect the registration of
Registrable Securities under the Securities Act (such registration upon such
request, a "Demand Registration"), provided that such request shall relate to
an amount of Registrable Securities at least equal to 25% of the total amount
of Registrable Securities.

       (b)    Within ten days after receipt of a request for the Demand
Registration, the Company shall give written notice (the "Notice") of such
request to all other Holders and shall include in such registration (except as
otherwise provided herein) all Registrable Securities for which the Company has
received,





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within 15 days after receipt by the applicable Holder of the Notice, a written
request to be included therein.  All requests made under this Section 3(b)
shall specify the aggregate number of Registrable Securities to be registered.

       (c)    A registration shall not constitute a Demand Registration until
it has become effective.  In any registration initiated as a Demand
Registration, the Company shall pay all Registration Expenses incurred in
connection therewith, whether or not such Demand Registration becomes
effective; provided that a Holder participating in such registration shall pay
all Registration Expenses if such Demand Registration fails to become effective
solely as a result of an act or omission by such Holder.

       (d)    The Company shall only be obligated to effect one Demand
Registration.

       (e)    The Holder of a majority of the Registrable Securities shall have
the right to decide whether or not the offering of the securities will be an
underwritten offering and shall have the right to choose such underwriter or
underwriters.

       4.     Piggy-back Registration.

       (a)    If, at any time, the Company proposes to file a registration
statement under the Securities Act with respect to an offering by the Company
for its own account or for the account of any security holders of the Company
of any class of debt or equity security of the Company (other than a
registration statement on Form S-4 or S-8 or any successor or similar forms
thereto), which is anticipated to be or becomes effective on or after May 30,
1997, the Company shall give written notice of such proposed filing (the
"Offering Notice") to Drillships and to all holders of Registrable Securities
to whom the transfer of Registrable Securities have, from time to time, been
registered on the books and records of the Company (Drillships and any such
transferee each referred to herein as a "Holder" and collectively as
"Holders"), such securities so transferred constituting Registrable Securities
immediately following such transfer, at least 30 days before the date of
anticipated filing with the Commission. Such Offering Notice shall offer to any
Holder, the opportunity, but in no event shall such offer constitute a
mandatory obligation, to register such number of Registrable Securities as any
such Holder may request in writing. For such request for registration (each a
"Piggyback Registration") to be effective it must be received by the Company
within 15 days after receipt by such Holder of the Offering Notice.

       (b)    In connection with any Piggy-back Registration, the Company shall
use best effort to cause the managing underwriter or underwriters of a proposed
underwritten offering to permit any Holder of the Registrable Securities who
requested to be included in the registration for such offering to include such
Registrable Securities in such offering on the same terms and conditions as any
similar securities of the Company or, if such offering is for the account of
other security holders, any similar securities of such security holders
included therein.  Notwithstanding the foregoing, if the managing underwriter
or underwriters of a proposed underwritten offering advise the Company in
writing that in its or their opinion the number of Registrable Securities
proposed to be sold in such offering exceeds the number of Registrable
Securities that can be sold in such offering without adversely affecting the
market for the Common Stock, the Company will include in such registration the
number of Registrable Securities that in the opinion of such managing
underwriter or underwriters can be sold without adversely affecting the market
for the Common Stock.  In such event, the Company shall reduce the number of
Registrable Securities to be offered for the accounts of any Holder pro rata on
the basis of the relative number of any Registrable Securities requested by
each Holder to be included in such registration to the extent necessary





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<PAGE>   5
to reduce the total number of Registrable Securities to be included in such
offering to the number recommended by such managing underwriter or
underwriters; provided however, that any such reduction in the number of
Registrable Securities shall not constitute a Piggy-back Registration.  The
Company shall pay all Registration Expenses incurred in connection with a
Piggy-back Registration.

       (c)    The Holders of Registrable Securities shall be entitled to
participate in no more than two Piggy-back Registrations.

       5.     Certain Matters Concerning Demand Registrations.

       (a)    Notwithstanding anything in the foregoing Sections 3(a) and 4(a),
if the Company's Board of Directors reasonably determines that a Demand
Registration would substantially interfere with a material transaction being
considered by the Company, the Company may delay such Demand Registration for
30 days.

       (b)    The Company may, if permitted by law, effect any Demand
Registration by the filing of a registration statement on Form S-3 (or any
successor or similar short-form registration statement).

       (c)    A Demand Registration shall not be deemed to have been effected
unless it becomes effective with the Commission, provided that a registration
which does not become effective after the Company filed a registration
statement with respect thereto with the Commission solely by reason of any
participating Holder failing to proceed shall be deemed to have been effected
by the Company in satisfaction of the obligation of the Company to register
Registrable Securities pursuant to the Demand Registration, unless the Company
shall have been promptly reimbursed for all Registration Expenses by the Person
who demanded registration and failed to proceed.  If a Demand registration has
been initiated, the failure of any Holder to proceed with such registration
shall not constitute a revocation of the request for registration nor relieve
the Company of its obligation to effect such Demand Registration as to
Registrable Securities of any other Holder who has elected to participate in
such Demand Registration and who proceeds therewith.  Notwithstanding the
foregoing, a registration statement will not be deemed to have been effected if
after it becomes effective with the Commission, such registration is interfered
with by any stop order, injunction or other order or requirement of the
Commission or other governmental agency or any court proceeding for any reason
other than a misrepresentation or omission by the Holder initiating the demand.


       6.     Registration Procedures; Damages.

       (a)    If and whenever any Holder of Registrable Securities have
requested that any Registrable Securities be registered pursuant to Section 3
or 4, the Company shall use its best efforts to effect the registration of such
Registrable Securities under the Securities Act and in accordance with the
intended method of disposition thereof as expeditiously as practicable and in
connection with any such request will, as expeditiously as possible:

       (i)    in connection with a Demand Registration, prepare and file with
the Commission, as soon as practicable, but in any event not later than 60 days
after receipt of a request to file a registration statement with respect to
Registrable Securities, a registration statement on any form for which the
Company then qualifies or which counsel for the Company and the Holder's
Counsel (as hereinafter defined) shall deem appropriate and which form shall be
available for the sale of such Registrable





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Securities in accordance with the intended method of distribution thereof and,
if the offering is an underwritten offering, shall be reasonably satisfactory
to the managing underwriter or underwriters, and use its best efforts to cause
such registration statement to become effective; provided, however, that before
filing a registration statement or prospectus or amendments or supplements
thereto, the Company shall (a) furnish to the counsel (the "Holder's Counsel")
selected by the Holder making the demand, or if no demand is made, the holders,
in the aggregate, of a majority of the Registrable Securities covered by such
registration statement, copies of all documents proposed to be filed a
reasonable period of time prior to the filing thereof, which documents will be
subject to the review and comment of such counsel and each seller of
Registrable Securities included in such registration statement, and (b) notify
each seller of Registrable Securities of any stop order, injunction or other
order or requirement issued or threatened by the Commission or other
governmental agency or any court injunction and take all reasonable actions
required to prevent the entry of such stop order, injunction or other order or
requirement or to remove it if entered; provided further, that in no event
shall the Company be under any obligation to cause a Demand Registration to
become effective prior to May 30, 1997;

       (ii)   in connection with a registration pursuant to Section 3 or 4,
prepare and file with the Commission such amendments and supplements to such
registration statement and the prospectus used in connection therewith as may
be necessary to keep such registration statement effective for a period of not
less than 90 days (or such shorter period that will terminate when all
Registrable Securities covered by such registration statement have been sold,
but not before the expiration of the applicable period referred to in Section
4(3) of the Securities Act and Rule 174 thereunder, if applicable), and comply
with the provisions of the Securities Act applicable to it with respect to the
disposition of all securities covered by such registration statement during
such period in accordance with the intended methods of disposition by the
sellers thereof set forth in such registration statement;

       (iii)  furnish to each seller of Registrable Securities one signed copy
of the registration statement and each amendment thereto as filed with the
Commission, and such number of copies of such registration statement,
amendments and supplements thereto (in each case including all exhibits
thereto), the prospectus included in such registration statement (including
each preliminary prospectus) and such other documents as such seller may
reasonably request in order to facilitate the disposition of the Registrable
Securities owned by them;

       (iv)   use all reasonable efforts to register or qualify such
Registrable Securities under such other securities or "blue sky" laws of such
jurisdictions as any seller or underwriter reasonably requests in writing and
do any and all other acts and things that may be reasonably necessary or
advisable to qualify for sale in such jurisdictions the Registrable Securities
owned by such seller; provided, however, that the Company shall not be required
(a) to qualify generally to do business in any jurisdiction where it is not
then so qualified, (b) to subject itself to jurisdiction or qualification in
any such jurisdiction, (c) to consent to general service of process in any such
jurisdiction, (d) to provide any undertaking required by such other securities
or "blue sky" laws or (e) make any change in the charter or bylaws that the
Board of Directors determines in good faith to be contrary to the best interest
of the Company and its stockholders;

       (v)    use all reasonable efforts to cause the Registrable Securities
covered by such registration statement to be registered with or approved by
such other governmental agencies or authorities as may be necessary by virtue
of the business and operations of the Company to enable the sellers thereof or
the underwriters, if any, to consummate the disposition of such Registrable
Securities;





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       (vi)   notify each seller of such Registrable Securities and the
Holder's Counsel at any time when a prospectus relating thereto is required to
be delivered under the Securities Act of the happening of any event as a result
of which the prospectus included in such registration statement contains an
untrue statement of a material fact or omits to state any material fact
required to be stated therein or necessary to make the statement therein, in
light of the circumstances under which they were made, not misleading, and
prepare and file with the Commission a supplement or amendment to such
prospectus after prompt review by the Holder's Counsel so that, as thereafter
delivered to the purchasers of such Registrable Securities, such prospectus
will not contain an untrue statement of a material fact or omit to state any
material fact required to be stated therein or necessary to make the statement
therein, in light of the circumstances under which they were made, not
misleading;

       (vii)  enter into customary agreements in form and substance reasonably
satisfactory to the Company (including an underwriting agreement in customary
form for companies of similar size and credit rating, if the offering is an
underwritten offering) and take in good faith such other actions as are
reasonably required in order to expedite or facilitate the disposition of such
Registrable Securities, including making presentations to brokers, analysts and
potential purchasers, in each case as if the Company were the seller of the
Registrable Securities;

       (viii)  make available for inspection by any seller of Registrable
Securities, any underwriter participating in any disposition pursuant to such
registration statement, the Holder's Counsel and any attorney, accountant or
other agent retained by any such seller or underwriter (collectively, the
"Inspectors"), all financial and other records, pertinent corporate documents
and properties of the Company (collectively, the "Records") and provide
reasonable access during normal business hours to officers, directors,
employees and agents to ask questions, in each ease as shall be reasonably
necessary to enable the Inspectors to exercise their due diligence
responsibility, and cause the Company's officers, directors, employees and
agents to supply all information reasonably requested and to answer all
questions reasonably asked by any such Inspector in connection with such
registration statement.  Records that the Company determines, in good faith, to
be confidential and that it notifies the Inspectors are confidential shall not
be disclosed by the Inspectors unless (a) the disclosure of such records is, in
the reasonable opinion of Holder's Counsel, necessary to avoid or correct a
misstatement or omission of a material fact in the registration statement,
provided that any such Holder has notified the Company of such condition and
has afforded the Company an opportunity to correct any such misstatement or
omission, or (b) the release of such records is required (in the written
opinion of counsel of such seller or underwriter, which counsel shall be
reasonably acceptable to the Company) pursuant to applicable state or federal
law.  The seller of Registrable Securities agrees that it will deliver such
opinion to the Company a reasonable period before releasing such information
and, upon learning that disclosure of such records is sought by a court or
governmental agency, provide notice to the Company and, in each case, allow the
Company, at the Company's expenses, to undertake an appropriate action to
prevent disclosure of the records deemed confidential;

       (ix)   if such sale is pursuant to an underwritten offering, use all
reasonable efforts to obtain a "cold comfort" letter and updates thereof from
the Company's independent public accountants in customary form and covering
such matters of the type customarily covered by "cold comfort" letters as the
holders, in the aggregate, of a majority of the Registrable Securities being
sold and the managing underwriter or underwriters reasonably request;

       (x)    otherwise use all reasonable efforts to comply with all
applicable rules and regulations of





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the Commission, and make generally available to its security holders, as soon
as reasonably practicable, an earnings statement covering a period of 12
months, beginning within three months after the effective date of the
registration statement, which earnings statement shall satisfy the provisions
of Section 11(a) of the Securities Act;

       (xi)   use all reasonable efforts to cause all Registrable Securities
covered by the registration statement to be listed on each securities exchange,
if any, on which similar securities issued by the Company are then listed,
provided that the applicable listing requirements are satisfied;

       (xii)  provide a transfer agent and registrar for all such Registrable
Securities not later than the effective date of such registration statement;
and

       (xiii)  cause counsel to the Company to provide customary legal opinions
reasonably requested by the Holders holding, in the aggregate, of a majority of
the Registrable Securities being sold.

       The Company may request each seller of Registrable Securities as to
which any registration is being effected to furnish to the Company such
information regarding the distribution of such securities and other matters as
may be reasonably required to be included in the registration statement and
each seller of Registrable Securities shall have the opportunity to review and
approve the presentation of such material in the registration statement.  In
addition, any Holder of Registrable Securities will have the right to propose a
plan of distribution section of the registration statement/prospectus in the
form attached hereto as Exhibit A.  The Company shall promptly notify the
Holder's Counsel of any request by the Commission for any amendment or
supplement of such registration statement or prospectus or for additional
information and shall promptly notify each seller of Registrable Securities of
any such request by the Commission if such request pertains directly to the
material set forth in the preceding sentence.  The Company shall promptly
notify each seller of Registrable Securities and the Holder's Counsel after the
Company shall receive notice of the time when such registration statement
became effective or when any amendment or supplement referred to in the
preceding sentence is filed.

       Each Holder of Registrable Securities agrees that, upon receipt of any
notice from the Company of the happening of any event of the kind described in
Paragraph (vi) of this Section 6(a), each such Holder shall forthwith
discontinue disposition of Registrable Securities pursuant to the registration
statement covering such Registrable Securities until such Person's receipt of
the copies of the supplemented or amended prospectus contemplated by paragraph
(vi) of this Section 6(a), and, if so directed by the Company, such Person
shall deliver to the Company (at the Company's expense) all copies, other than
permanent file copies then in such Holder's possession, of the prospectus
covering such Registrable Securities current at the time of receipt of such
notice.  If the Company shall give any such notice, the Company shall extend
the period during which such registration statement shall be maintained
effective pursuant to this Agreement (including the period referred to in
paragraph (ii) of this Section 6(a)) by the number of days during the period
from and including the date of the giving of such notice pursuant to paragraph
(vi) of this Section 6(a) to and including the date when each seller of
Registrable Securities covered by such registration statement shall have
received the copies of the supplemented or amended prospectus contemplated by
paragraph (vi) of this Section 6(a).

       (b)    The Company may require each Holder, at Company's expense, to
furnish the Company with such information and undertakings as it may reasonably
request regarding each such Holder and the distribution of such securities as
the Company may from time to time reasonably request in writing.





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<PAGE>   9
       7.     Underwritten Offerings.

       (a)    If a Demand Registration is an underwritten offering, if
requested by the underwriters, the Company will enter into an underwriting
agreement with the managing underwriter or underwriters for such offering
(which managing underwriter or underwriters shall be an investment banking firm
or firms of national reputation), such agreement to be in form and substance
reasonably satisfactory to the Company and to Holder's Counsel and to contain
such representations and warranties by the Company and such other terms as are
customarily contained in agreements of such type, including, without
limitation, indemnities to the effect and to the extent provided in Section 8.
The sellers of Registrable Securities in such offering shall be party to such
underwriting agreement and may require that any or all of the representations
and warranties by, and the other agreements on the part of, the Company to and
for the benefit of such underwriters shall also be made to and for the benefit
of such sellers and that any or all of the conditions precedent to the
obligations of such underwriters under such underwriting agreement be
conditions precedent to the obligation of such sellers.  No Holder shall be
required to make any representations or warranties to or agreements with the
Company or the underwriters other than representations, warranties or
agreements regarding such Person, its ownership of Registrable Securities and
its intended method of distribution and any other representation required by
applicable law.

       (b)    Each Holder of Registrable Securities agrees by acquisition of
such Registrable Securities, if so required by the managing underwriter, not to
effect any public sale or distribution of Registrable Securities or sales of
such Registrable Securities pursuant to Rule 144 or Rule 144A under the
Securities Act, during the 14 days prior to and the 90 days after any firm
commitment underwritten registration pursuant to Section 3 or 4 has become
effective (except as part of such registration) or, if the managing underwriter
advises the Company that in its opinion, no such public sale or distribution
should be effected for a period of 120 days after such underwritten
registration in order to complete the sale and distribution of securities
included by such registration and the Company gives written notice to each
Holder of such advice.  Each such Person shall not effect any public sale or
distribution of Registrable Securities or sales of such Registrable Securities
pursuant to Rule 144 or Rule 144A under the Securities Act during such 120-day
period after such underwritten registration, except as part of such
underwritten registration, whether or not such Person participates in such
registration.

       8.     Indemnification.

       (a)    The Company will, and hereby does, agree to indemnify and hold
harmless, to the full extent permitted by law, Drillships and each Holder, and
each other Person, if any, who controls Drillships or such Holder within the
meaning of the Securities Act, against any losses, claims, damages or
liabilities (or actions in respect thereof), joint or several, to which
Drillships or any Holder or any such director, partner, member, manager,
officer, employee, agent or other controlling Person or Drillships or its
controlling Persons may become subject under the Securities Act or otherwise,
insofar as such losses, claims, damages or liabilities (or actions or
proceedings, whether commenced or threatened, in respect thereof) arise out of
or are based upon (i) any untrue statement or alleged untrue statement of any
material fact contained in any registration statement under which such
securities were registered under the Securities Act, any preliminary
prospectus, final prospectus or summary prospectus contained therein or any
document incorporated therein by reference, or any amendment or supplement
thereto, or any omission or alleged omission to state therein a material fact
required to be stated therein or necessary to make such statements therein (in
the case of a prospectus, in light of the circumstance under which they





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<PAGE>   10
were made) not misleading, or (ii) any violation by the Company or any of its
officers, directors, employees, representatives or agents of any rule or
regulation under applicable securities laws or other laws applicable to the
Company, in each case, the Company will reimburse Drillships, any Holder and
each such director, partner, member, manager, officer, employee, agent and
controlling Person of Drillships or its controlling Persons for any legal and
any other expenses reasonably incurred by them in connection with investigating
or defending any such loss, claim, liability, action or proceeding; provided
that the Company shall not be liable in any such case to the extent that any
such loss, claim, damage, liability (or action or proceeding in respect
thereof) or expense arises out of or is based upon an untrue statement or
alleged untrue statement or omission or alleged omission made in such
registration statement, any such preliminary prospectus, final prospects,
summary prospectus, amendment or supplement in reliance upon and in conformity
with information furnished in writing to the Company by Drillships or any such
Holder.

       (b)    Drillships and each Holder will, and hereby does, agree to
provide the Company with an undertaking to indemnify and hold harmless,
severally and not jointly, to the full extent permitted by law, the Company,
its directors, officers and each other Person, if any, who controls the Company
(within the meaning of the Securities Act), against any losses, claims, damages
or liabilities, joint or several, to which the Company or any such director,
officer or controlling Person may become subject under the Securities Act or
otherwise, insofar as such losses, claims, damages or liabilities (or actions
or proceedings, whether commenced or threatened, in respect thereof) arise out
of or are based upon any untrue statement or alleged untrue statement of any
material fact or any omission or alleged omission of a material fact required
to be stated in any registration statement under which such securities were
registered under the Securities Act, any preliminary prospectus, final
prospectus or summary prospectus contained herein or any document incorporated
therein by reference, or any amendment or supplement hereto, or any omission or
alleged omission to state therein a material fact required to be stated therein
or necessary to make the statements therein (in the case of a prospectus, in
light of the circumstances under which they were made) not misleading, only to
the extent, such statement or alleged statement or omission or alleged omission
was made in reliance upon and in conformity with information furnished in
writing to the Company solely by Drillships or any such Holder.

       (c)    Promptly after receipt by an indemnified party of notice of any
threatened action or proceeding or the commencement of any action or proceeding
involving a claim referred to in the preceding subsections of this Section 8,
such indemnified party will, if a claim in respect thereof is to be made
against an indemnifying party, give written notice to the latter of the threat
or commencement of such action or proceeding, provided that the failure of any
indemnified party to give notice as provided herein shalt not relieve the
indemnifying party of its obligations under the preceding subsections of this
Section 8, except to the extent that the indemnifying party is actually
prejudiced by such failure to give notice.  In case any such action is brought
against an indemnified party, unless in such indemnified party's reasonable
judgment a conflict of interest between such indemnified and indemnifying
parties may exist in respect of such claim, the indemnifying party shall be
entitled to participate in and to assume the defense thereof, jointly with any
other indemnifying party similarly notified to the extent that it may wish,
with counsel reasonably satisfactory to such indemnified party, and after
notice from the indemnifying party to such indemnified party of its election to
so assume the defense thereof, the indemnifying patty shall not be liable to
such indemnified company for any legal or other expenses subsequently incurred
by the latter in connection with the defense thereof other than reasonable
costs of investigation.  No indemnifying party shall consent to entry of any
judgment or enter into any settlement without the consent of the indemnified
company which does not include as an unconditional term thereof the giving by
the claimant or plaintiff to





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<PAGE>   11
such indemnified party of a release from all liability in respect of such claim
or litigation.

       (d)    Indemnification similar to that specified in the preceding
subsections of this Section 8 (with appropriate modifications) shall be given
by the Company and the sellers of Registrable Securities with respect to any
required registration or other qualification of securities under any Federal or
state law or regulation of any governmental authority, other than the
Securities Act.

       (e)    If the indemnification provided for in this Section 8 from the
indemnifying party is unavailable to an indemnified party hereunder in respect
of any losses, claims, damages, liabilities or expenses referred to herein,
then the indemnifying party, to the extent such indemnification is unavailable,
in lieu of indemnifying such indemnified party, shall contribute to the amount
paid or payable by such indemnified party as a result of such losses, claims,
damages, liabilities or expenses in such proportion as is appropriate to
reflect the relative fault of the indemnifying party and indemnified parties in
connection with the actions that resulted in such losses, claims, damages,
liabilities or expenses.  The relative fault of such indemnifying party and
indemnified parties shall be determined by reference to, among other things,
whether any action in question, including any untrue or alleged untrue
statement of a material fact or omission or alleged omission to state a
material fact, has been made by, or relates to information supplied by, such
indemnifying party or indemnified parties, and the parties' relative extent of
knowledge, access to information and opportunity to correct or prevent such
action.  The amount paid or payable by a party as a result of the losses,
claims, damages, liabilities and expenses referred to above shall be deemed to
include any legal or other fees or expenses reasonably incurred by such party
in connection with any investigation or proceeding.

       The parties hereto agree that it would not be just and equitable if
contribution pursuant to this Section 8(e) were determined by pro rata
allocation or by any other method of allocation that does not take account of
the equitable considerations referred to in the immediately preceding
paragraph.  No Person guilty of fraudulent misrepresentation (within the
meaning of Section 10(f) of the Securities Act) shall be entitled to
contribution from any Person.

       If indemnification is available under this Section 8, the indemnifying
parties shall indemnify each indemnified party to the full extent provided in
Sections 8(a) and 8(b) without regard to the relative fault of said
indemnifying parties or indemnified party or any other equitable consideration
provided for in this Section 8.

       (f)    The indemnification or contribution required by this Section 8
shall be made by periodic payments of the amount thereof during the course of
the investigation or defense, as and when bills are received or expense, loss,
damage or liability is incurred.

       9.     Covenants Relating to Rule 144.  The Company covenants that it
shall use its best efforts to file the reports required to be filed by it under
the Securities Exchange Act of 1934, as amended, and the rules and regulations
of the Commission thereunder for so long as the Company becomes obligated to
file such reports (or, if the Company ceases to be required to file such
reports, it shall, upon the request of any Holder, make publicly available
other information so that Rule 144 shall be available to any Holder), and it
shall, if feasible, take such further action as any Holder may reasonably
request, all to the extent required from time to time to enable such Person to
sell Registrable Securities without registration under the Securities Act
within the limitation of the exemptions provided by (a) Rule 144 or Rule 144A
under the Securities Act, as such Rules may be amended from time to time, or
(b) any similar rules or





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<PAGE>   12
regulations hereafter adopted by the Commission.  Upon the request of any
Holder, the Company shall deliver to such Person a written statement as to
whether it has complied with such requirement.

       10.    Miscellaneous.

       (a)    Specific Performance.  The parties hereto acknowledge that there
may be no adequate remedy at law if any party fails to perform any of its
obligations hereunder and that each party may be irreparably harmed by any such
failure, and accordingly agree that each party, in addition to any other remedy
to which it may be entitled at law or in equity, shall be entitled to compel
specific performance of the obligations of any other party under this Agreement
in accordance with the terms and conditions of this Agreement.

       (b)    Notices.  All notices, requests, claims, demands, waivers and
other communications hereunder shall be in writing md shall be deemed to have
been duly given when delivered by hand, if delivered personally by courier, or
by telecopy or ten (10) days after being deposited in the mail (registered or
certified mail, postage prepaid, return receipt requested) as follows: if to
the Company, to it at 1900 West Loop South, Suite 1800, Houston, Texas 77027,
Attention: Steven A. Webster and if to Drillships, to it at c/o Wexford
Management LLC, 411 West Putnam Avenue, Greenwich, CT 06830, Attention: Spyros
Skouras and if to a Holder, to its address as indicated on the Company's
register or stock ledger or other books or records, or to such other address as
any such Holder may have furnished to the Company in writing in accordance
herewith, except the notices of change of address shall be effective only upon
receipt.

       (c)    Governing Law and Arbitration.  THIS AGREEMENT SHALL BE GOVERNED
BY AND CONSTRUED IN ACCORDANCE WITH THE INTERNAL LAWS OF THE STATE OF NEW YORK.
Any dispute arising out of or in relation to this Agreement or the activities
conducted hereunder (whether tort or otherwise) shall be finally and
exclusively resolved by arbitration in New York, New York, in accordance with
the Rules of Arbitration of the American Arbitration Association by three
arbitrators.  The arbitration shall be conducted in the English language, and
each arbitrator shall have English as his or her first (mother-tongue)
language.  Disputes involving sums less than US$25,000 shall be resolved on the
basis of document submission alone by one arbitrator.  All decisions of the
arbitrator(s) shall be in writing, and the arbitrator(s) shall provide written
reasons for their decisions.  The arbitration shall be final and binding on the
parties.  The prevailing party shall be entitled to recover from the losing
party reasonable expenses, attorneys' fees and costs.

       (d)    Headings.  The descriptive headings of the several Sections and
paragraphs of this Agreement are inserted for convenience only, and do not
constitute a part of this Agreement and shall not affect in any way the meaning
or interpretation of this Agreement.

       (e)    Entire Agreement; Amendments.  This Agreement and the other
writings referred to herein or delivered pursuant hereto which form a part
hereof and contain the entire understanding of the parties with respect to its
subject matter.  This Agreement supersedes all prior agreements and
understandings between the parties with respect to its subject matter.  This
Agreement may be amended and the observance of any term of this Agreement may
be waived (either generally or in a particular instance and either
retroactively or prospectively) only by a written instrument duly executed by
the Company, Drillships and any Holder.  Drillships and any other Holder shall
be bound by an amendment or waiver authorized by this Section 10(e), whether or
not any Registrable Securities held by such Person





                                       12
<PAGE>   13
shall, have been marked to indicate such consent.

       (f)    Assignability of Registration Rights.  The rights and benefits
accruing to, and the obligations of, any Holder hereunder shall be freely
assignable in connection with and shall attach to any transfer of Registrable
Securities to any Person provided that any of such rights, benefits and
obligations shall be effective only to the extent set forth herein and that,
except as set forth in Section 4, no individual holder of a Registrable
Security shall have any rights, benefits or obligations hereunder unless such
individual holder constitutes a Holder; and provided further that any Holder
effecting a transfer of the rights set forth in this Agreement, or who has
knowledge that any such transfer would cause any other Person or group of
Persons to have the rights of a Holder, shall provide the Company with notice
of such transfer and the identity of such Person or Persons.

       (h)    Counterparts.  This Agreement may be entered into in any number
of counterparts, and by the parties to it on separate counterparts, each of
which when so executed and delivered shall be an original, but all of which
together shall constitute one and the same instrument.

       (i)    Severability.  If any one or more of the provisions contained
herein, or the application thereof in any circumstances, is held invalid,
illegal or unenforceable in any respect for any reason, the validity, legality
and enforceability of any such provision in every other respect and of the
remaining provisions hereof shall not be in any way impaired, it being intended
that all of the rights of Drillships or any other Holder shall be enforceable
to the fullest extent permitted by law.

       (j)    Written Consent.  The Company, Drillships and each Holder agree
that whenever in this Agreement the written consent of any party is required,
such written consent shall not be unreasonably withheld or delayed.


              IN WITNESS WHEREOF, the parties have executed this Agreement as
of the date first written above.



                                      FALCON DRILLING COMPANY, INC.




                                      By      /s/ LEIGHTON E. MOSS  
                                        ----------------------------------------
                                          Name:   Leighton E. Moss
                                          Title:  V.P.


                                      KS DEEPSEA DRILLSHIPS



                                      By      /s/ SPYROS SKOURAS
                                        ----------------------------------------
                                          Name:   Spyros Skouras 
                                          Title:





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<PAGE>   14
                                                                       EXHIBIT A


                              PLAN OF DISTRIBUTION


       The Common Stock may be sold from time to time by the Selling
Stockholders, or by pledgees, donees, transferees or other successors in
interest.  Such sales may be made on one or more exchanges or in the over-the-
counter market, or otherwise at prices and at terms then prevailing or at
prices related to the then current market price, or in negotiated transactions.
The shares may be sold by one or more of the following:  (a) a block trade in
which the broker or dealer so engaged will attempt to sell the shares as agent
but may position and resell a portion of the block as principal to facilitate
the transaction; (b) purchases by a broker or dealer as principal and resale by
such broker or dealer for its account pursuant to this Prospectus; (c) an
exchange distribution in accordance with the rules of such exchange; and (d)
ordinary brokerage transactions and transactions in which the broker solicits
purchasers.  In addition, any securities covered by this Prospectus which
qualify for sale pursuant to Rule 144 may be sold under Rule 144 rather than
pursuant to this Prospectus.  From time to time the Selling Stockholders may
engage in short sales, short sales versus the box, puts and calls and other
transactions in securities of the issuer or derivatives thereof, and may sell
and deliver the shares in connection therewith.

       In effecting sales, brokers or dealers engaged by the Selling
Stockholders may arrange for other brokers or dealers to participate.  Brokers
or dealers will receive commissions or discounts from Selling Stockholders in
amounts to be negotiated immediately prior to the sale.  The Selling
Stockholders and agents who execute orders on their behalf may be deemed to be
underwriters as that term is defined in Section 2(11) of the Act and a portion
of any proceeds of sales and discounts, commissions or other compensation may
be deemed to be underwriting compensation for purposes of the Act.





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