<PAGE>   1
                                                                   EXHIBIT 10.35


                            RESTRUCTURING AGREEMENT


         This Restructuring Agreement is dated as of September 22, 1997 by and
between DeepTech International Inc.  ("DeepTech"), a Delaware corporation, and
Tatham Offshore, Inc. ("Tatham Offshore"), a Delaware corporation.  DeepTech
and Tatham Offshore may be referred to herein collectively as the "Parties" or
individually as a "Party."

                                    RECITALS

         WHEREAS, Tatham Offshore issued to DeepTech the Notes (defined herein)
under which Tatham Offshore makes periodic interest payments;

         WHEREAS, Tatham Offshore has proposed, and DeepTech has accepted, an
arrangement whereby DeepTech will forgive the next two scheduled payments under
the Notes and, on or before January 31, 1998, return the Notes to Tatham
Offshore in consideration for the right to exercise one of three options; and

         WHEREAS, under such options, DeepTech has the right to receive (i)
common stock of Tatham Offshore, (ii) all of the capital stock of TODI (defined
herein), certain rights under the Drilling Order (defined herein) and cash, or
(iii) preferred stock of Tatham Offshore and cash;

         NOW, THEREFORE, for and in consideration of the premises and the
mutual covenants and agreements contained herein and other good and valuable
consideration (the receipt and sufficiency of which are hereby confirmed and
acknowledged), the Parties hereto hereby stipulate and agree as follows:


                                   ARTICLE I.
                                  DEFINITIONS

     1.1 SPECIFIC DEFINITIONS.  The following capitalized terms shall have the 
meanings ascribed to them in this Section 1.1.

         "Acquired Stock" means any Common Stock or Senior Preferred Stock
acquired by DeepTech pursuant to Article II.

         "Affiliate" means, with respect to any relevant Person, or any other
Person that directly or indirectly controls, is controlled by or is under
common control with, such relevant Person in question.  For purposes of this
definition, the term "control" (including its derivatives and similar terms)
means the direct or indirect ability to direct the management and policy of the
relevant Person, whether by ownership or control of voting interests, contract
or otherwise.

<PAGE>   2
     "Agreement" means this Restructuring Agreement (including any exhibits,
supplements and other attachments), as amended, restated, supplemented or
otherwise modified from time to time.

     "Applicable Interest Payments" means all future interest payments due to
DeepTech from Tatham Offshore pursuant to Section 2.3 of the First Note and the
Second Note, including the payments due on October 1, 1997, and January 1,
1997.

     "Cash Equivalents" means cash, cash equivalents or unrestricted, freely
tradable marketable securities issued by an "investment grade" company listed
on the New York Stock Exchange, the American Stock Exchange or the NASDAQ.

     "Commission" means the Securities and Exchange Commission or any other
federal agency then administering the Securities Act, the Exchange Act, and
other federal securities laws.

     "Common Stock" means common stock, $0.01 par value per share, with one
vote per share, issued by Tatham Offshore, as adjusted from time to time to
reflect any reorganization or recapitalization, including, without limitation,
the issuance or cancellation of shares in connection with a stock split or
stock dividend.

     "DeepTech" shall have the meaning ascribed to it in the preamble to this
Agreement.

     "DeepTech Holder" means either DeepTech or, if DeepTech is not a Holder,
any Affiliate of DeepTech which is a Holder.

     "Demand Registration" shall have the meaning ascribed to it in Section
1.(a) of Exhibit "B".

     "Drilling Order" means that certain drilling order dated September 19,
1996 by and between Tatham Offshore and Sedco, as further modified by that
certain letter agreement dated August 14, 1997 and executed August 29, 1997
between Tatham Offshore and Sedco.

     "Exchange Act" means the Securities Exchange Act of 1934, as amended from
time to time.

     "Farm-Out" means an agreement or other arrangement in which the owner
of a working interest in an oil and gas lease or similar instrument delivers
the contractual right to earn an interest in such oil and gas lease or similar
instrument to another party in exchange for such other party (i) satisfying
certain obligations, (ii) performing or causing the performance of certain
actions and/or (iii) satisfying certain conditions.


                                           2
<PAGE>   3
         "First Note" means that certain 11 3/4% Subordinated Convertible
Promissory Note dated February 14, 1994 in the amount of $34,000,000 issued by
Tatham Offshore to DeepTech, as amended, restated, supplemented or otherwise
modified from time to time.

         "Holder" means any holder of any Acquired Stock.

         "Inspectors" shall have the meaning ascribed to it in Section 3.a.(vi)
of Exhibit B.

         "Laws" means the laws, rules, regulations, decrees and orders of the
United States of America and all other governmental authorities having
jurisdiction, whether such Laws now exist or hereafter come into effect.

         "Lien" means mortgages, deeds of trust, liens, pledges, security
interests, leases, conditional sale contracts, claims, rights of first refusal,
options, charges, liabilities, obligations, agreements, privileges, liberties,
easements, rights-of-way, limitations, reservations, restrictions and other
defects or encumbrances of any kind.

         "Market Price" means (i) if there shall then be a public market for
the Common Stock, the average of the closing prices for the ten (10) trading
days immediately preceding the date on which DeepTech delivers or is deemed to
have delivered the notice contemplated by Section 2.6, or (ii) if there shall
then be no public market for the Common Stock, the value as of the date on
which DeepTech delivers or is deemed to have delivered the notice contemplated
by Section 2.6 as determined by an appraisal of the Common Stock conducted by a
nationally-reputable qualified independent appraiser.

         "Note Purchase Agreement" means that certain Subordinated Convertible
Note Purchase Agreement dated as of February 14, 1994 by and between Tatham
Offshore and DeepTech, as amended, restated, supplemented or otherwise modified
from time to time.

         "Notes" means, collectively, the First Note and the Second Note.

         "Option" shall have the meaning ascribed to it in Section 2.2.

         "Option Exercise Period" shall have the meaning ascribed to it in
Section 2.5.

         "Option Expiration Time" shall have the meaning ascribed to it in
Section 2.5.

         "Party" or "Parties" shall have the meaning ascribed to it in the
preamble to this Agreement.


                                           3
<PAGE>   4
         "Permitted Transaction" means any transaction, or series of related
transactions, (i) providing fair value and (ii) the terms of which are no less
favorable than could be obtained from a non-Affiliated Person in an arms-length
transaction.

         "Person" means any individual or entity, including, without
limitation, any corporation, limited liability company, partnership (general or
limited), joint venture, association, joint stock company, trust,
unincorporated organization or government (including any board, agency,
political subdivision or other body thereof).

         "Records" shall have the meaning ascribed to it in Section 3.a.(vi) of
Exhibit B.

         "Registered Security Holders" shall have the meaning ascribed to it in
Section 2 of Exhibit B.

         "Registrable Securities" means each share evidenced by any Acquired
Stock from the date of issuance pursuant to this Agreement until the earlier to
occur of (i) the date on which such share of Acquired Stock ceases to be a
Restricted Security or (ii) the date on which a Demand Registration is effected
pursuant to Exhibit B.

         "Registration Expenses" shall have the meaning ascribed to it in
Section 4 of Exhibit B.

         "Restricted Security" means each share evidenced by any Acquired Stock
until the earlier to occur of the date on which (i) a registration statement
covering such share has been declared effective and it has been disposed of
pursuant to such effective registration statement, (ii) it is sold pursuant to
Rule 144 (or any similar provisions then in force) under the Securities Act, or
(iii) it has been otherwise transferred and Tatham Offshore has delivered new
certificates or other evidences of ownership for them not subject to any legal
or other restriction on transfer under the Securities Act or under state
securities laws and not bearing the legend specified in Section 3.1.

         "Second Note" means that certain 11 3/4% Subordinated Convertible
Promissory Note dated June 30, 1994 in the amount of $26,000,000 issued by
Tatham Offshore to DeepTech, as amended, restated, supplemented or otherwise
modified from time to time.

         "Securities Act" means the Securities Act of 1933, as amended from
time to time.

         "Sedco" means Schlumberger Technology Corporation - Sedco Forex
Division.

         "Senior Preferred Stock" means the 6% Senior Preferred Stock having a
liquidation preference value equal to $60 million with the designated rights
and preferences set forth in that certain Certificate of Designation of
Preferences and Rights of 6% Senior Preferred Stock of Tatham Offshore attached
hereto as Exhibit "A."


                                           4
<PAGE>   5
         "Sunday Silence" means (i) the oil and gas property located in the
Outer Continental Shelf in the Gulf of Mexico and comprised of Ewing Bank
Blocks 958, 959, 1002 and 1003, which together constitute a field that is
comprised of 20,160 gross acres located approximately six miles south of Ewing
Bank Blocks 914 and 915 in water depths ranging from 1,400 to 1,600 feet and in
which Tatham Offshore has a 100% working interest, (ii) equipment, facilities,
wells or assets located thereon, used in connection therewith or related
thereto and owned by Tatham Offshore or TODI and (iii) any agreements, rights
or other arrangements related thereto and owned by Tatham Offshore or TODI (but
excluding the Drilling Order).

         "Tatham Offshore" shall have the meaning ascribed to it in the
preamble to this Agreement.

         "TODI" means Tatham Offshore Development, Inc., a Delaware corporation
which is wholly owned by Tatham Offshore.

         "TODI Interest" shall have the meaning ascribed to it in Section
4.3(a).

         "Transfer" or "Transferred" means a voluntary or involuntary sale,
assignment, transfer, conveyance, exchange, bequest, devise, gift or any other
alienation (in each case, with or without consideration) of any rights,
interests or obligations in the subject property.

         1.2     TERMS DEFINED IN THE NOTE PURCHASE AGREEMENT.  Capitalized
terms used in this Agreement, but not defined herein, shall have the meanings
ascribed to such terms in the Note Purchase Agreement.

         1.3     GENERAL DEFINITIONS.  Capitalized terms used in this Agreement
and not defined in Section 1.1 or the Note Purchase Agreement shall have the
meanings ascribed to them elsewhere in this Agreement.


                                  ARTICLE II.
                           RESTRUCTURING ARRANGEMENT

         2.1     FORBEARANCE.  DeepTech hereby relinquishes and forfeits its
right to receive, and forgives Tatham Offshore's obligation to pay, the
Applicable Interest Payments.

         2.2     RESTRUCTURING OPTION.  At any time during the Option Exercise
Period, DeepTech shall have the option (the "Option") to consummate any one of
the following transactions:

                                           5
<PAGE>   6
                 (a)      Conversion.  DeepTech may convert all or, to the
         extent provided in Section 2.3(b)(i), a portion of the principal
         amount outstanding under the Notes into shares of Common Stock at the
         Market Price; or

                 (b)      Sale of TODI.  Subject to Section 2.3,  Tatham
         Offshore shall sell for $60 million to DeepTech or an Affiliate of
         DeepTech (i) all of the outstanding capital stock of TODI and (ii) all
         of the right, title and interest of Tatham Offshore under the Drilling
         Order as it relates to the substitute rig in such agreement.  Tatham
         Offshore shall contemporaneously apply the proceeds from such sale to
         the prepayment in full of the Notes; or

                 (c)      Purchase of Senior Preferred Stock.  Tatham Offshore
         shall issue 6,000,000 shares of Senior Preferred Stock to DeepTech for
         $60 million payable in cash.  Tatham Offshore shall contemporaneously
         apply all of the proceeds from such issuance to the prepayment in full
         of the Notes.

         2.3     PRIOR TO EXERCISE OF OPTION.

                 (a)      Except to the extent expressly permitted in Section
         2.3(b) below, Tatham Offshore may not Transfer any interest in TODI or
         the Drilling Order or allow TODI to Transfer any interest in Sunday
         Silence prior to exercise or deemed exercise of the Option.

                 (b)      Prior to the exercise of the Option by DeepTech,
         Tatham Offshore may:

                          (i)     Sell all (but not a portion) of its interest
         in TODI or allow TODI to sell all (but not a portion) of TODI's
         interest in Sunday Silence.  In either case, such sale must be a
         Permitted Transaction for Cash Equivalents, without reserving any
         rights, title or interest (including, without limitation, any
         reversionary, back-in, overriding royalty, or working interest) of any
         kind.  Fifty percent (50%) of the proceeds of such sale shall be paid
         directly by the purchaser into an escrow account to which DeepTech is
         a party and held in escrow until DeepTech exercises or is deemed to
         have exercised the Option.  If such sale takes place, then in lieu of
         the transaction described in Section 2.2(b) above, DeepTech shall have
         the right to (i) require the escrow agent to apply the proceeds in
         escrow to the prepayment of the Notes and (ii) convert the remaining
         outstanding principal balance of the Notes into Common Stock at the
         Market Price pursuant to Section 2.2(a) above; or

                          (ii)    Permit TODI to enter into a Farm-Out in a
         Permitted Transaction with respect to Sunday Silence, provided that
         (A) any consideration paid in connection with such Farm-Out shall be
         paid directly into escrow and held in escrow until DeepTech exercises
         or is deemed to have exercised the Option, and (B) both the
         creditworthiness of the farmee and the development


                                           6
<PAGE>   7
         program contemplated by the Farmout are acceptable to DeepTech;
         provided, further, that DeepTech shall not unreasonably delay or
         withhold its consent with respect thereto.

         2.4     DEEMED EXERCISE. If DeepTech fails to timely deliver written
notice of its exercise of the Option as provided in Section 2.6, DeepTech will
be deemed to have exercised Section 2.2(b) of the Option effective as of the
Option Expiration Time.

         2.5     OPTION PERIOD.  The period during which the Option may be
exercised by DeepTech (the "Option Exercise Period") shall commence as of the
date hereof and terminate at midnight (the "Option Expiration Time") on
December 31, 1997, unless extended prior to such time by written request of the
board of Directors of DeepTech for a maximum of thirty (30) days.

         2.6      MANNER OF EXERCISE.  During the term of this Agreement,
DeepTech may exercise the Option by (i) delivering at any time prior to the
Option Exercise Time to Tatham Offshore written notice of the transaction in
Section 2.2 that it elects to consummate and (ii) in the case of the
transactions specified in Section 2.2(b) or 2.2(c), tender the purchase price
in immediately available funds to Tatham Offshore. Tatham Offshore shall
immediately apply any funds paid to it pursuant to (ii) to the prepayment in
full of the Notes. The Option shall also be deemed exercised if DeepTech fails
to deliver such notice and the election in Section 2.4 above is made. The
transaction contemplated by Section 2.2 shall be effective as of the exercise
or deemed exercise date thereof and shall be closed as soon as reasonably
practicable thereafter.

         2.7     ESCROW.  Prior to the time that DeepTech exercises or is
deemed to have exercised the Option, none of the proceeds deposited into escrow
pursuant to Sections 2.3(b)(i) or 2.3(b)(ii) shall be distributed without the
consent of DeepTech. If DeepTech exercises the Option, then the escrow agent
shall apply the proceeds to the outstanding principal and interest on the
Notes. If DeepTech is deemed to have exercised the Option, then the escrow
agent shall distribute the proceeds in any manner Tatham Offshore desires.

         2.8     GOVERNMENTAL CONSENT OR APPROVAL.  If any governmental consent
or approval is required in connection with the exercise of any of the Options,
DeepTech shall have a reasonable amount of time to obtain such consent or
approval. Tatham Offshore shall use reasonable, good faith efforts to
cooperate with DeepTech and to assist in timely obtaining such consent or
approval.


                                           7
<PAGE>   8
                                      ARTICLE III
                                      SECURITIES

         3.1     RESTRICTIVE LEGEND.  All Acquired Stock shall be Restricted
Securities and each certificate representing the Acquired Stock shall be
stamped or otherwise imprinted with a legend in substantially the following
form:

         THE SECURITIES REPRESENTED BY THIS CERTIFICATE HAVE NOT BEEN
         REGISTERED UNDER THE SECURITIES ACT OF 1933, AS AMENDED, OR THE
         SECURITIES LAWS OF ANY STATE.  WITHOUT SUCH REGISTRATION, SUCH
         SECURITIES MAY NOT BE SOLD, PLEDGED, HYPOTHECATED, OR OTHERWISE
         TRANSFERRED, EXCEPT UPON DELIVERY TO THE CORPORATION OF AN OPINION OF
         COUNSEL SATISFACTORY TO THE CORPORATION THAT REGISTRATION IS NOT
         REQUIRED FOR SUCH TRANSFER OR THE SUBMISSION TO THE CORPORATION OF
         SUCH OTHER EVIDENCE AS MAY BE SATISFACTORY TO THE CORPORATION TO THE
         EFFECT THAT ANY SUCH TRANSFER SHALL NOT BE IN VIOLATION OF THE
         SECURITIES ACT OF 1933, AS AMENDED, OR APPLICABLE STATE SECURITIES
         LAWS OR ANY RULE OR REGULATION PROMULGATED THEREUNDER.

         3.2     REGISTRATION RIGHTS.  The Holder of the Acquired Stock shall
have the right to require Tatham Offshore to register the Acquired Stock in
accordance with the terms and conditions set forth in Exhibit B attached
hereto.


                                      ARTICLE IV.
                            REPRESENTATIONS AND WARRANTIES

         4.1     REPRESENTATIONS AND WARRANTIES BY BOTH DEEPTECH AND TATHAM
OFFSHORE.  Each of the Parties, with respect to itself and its property, hereby
represents and warrants to the other as follows:

                 (a)      It is duly formed and validly existing and in good
         standing under the laws of the state of formation, with power and
         authority to carry on the business in which it is engaged and to
         perform its obligations under this Agreement.

                 (b)      The execution and delivery of this Agreement have
         been duly authorized and approved by all requisite corporate,
         partnership, limited liability company or other applicable action.


                                           8
<PAGE>   9
                 (c)      It has all the requisite corporate, partnership,
         limited liability company or other applicable power and authority to
         enter into this Agreement and perform its respective obligations
         hereunder and thereunder.

                 (d)      The execution and delivery of this Agreement do not,
         and consummation of the transactions contemplated herein will not,
         violate any of the provisions of its organizational documents or any
         agreement pursuant to which it is bound or, to its knowledge, any
         applicable Laws.

                 (e)      There are no pending suits or, to its knowledge,
         actions or other proceedings or suits which have been threatened to be
         instituted against it, in which it is a party and which affect the
         consummation of the transactions contemplated hereby or, in any
         material respect, its business or prospects.  It does not believe, in
         good faith, that any circumstances, events or conditions have occurred
         which reasonably could be expected (based on its knowledge and
         experience) to form the basis for a suit, action or other proceeding
         against it which, if adversely determined, reasonably could be
         expected to materially and adversely affect it.

                 (f)      This Agreement is, and will be, valid, binding and
         enforceable against it in accordance with its terms, subject to
         bankruptcy, moratorium, insolvency and other Laws generally affecting
         creditors' rights and general principles of equity (whether applied in
         a proceeding in a court of law or equity).

         4.2     REPRESENTATION AND WARRANTIES BY DEEPTECH.  DeepTech warrants
to Tatham Offshore as follows:

                 (a)      It has been furnished with such information about
         Tatham Offshore and the Common Stock and Preferred Stock as it has
         requested and with such information as necessary to comply with any
         and all applicable securities laws.

                 (b)      It has made its own independent inquiry and
         investigation into, and based thereon, has formed an independent
         judgment concerning Tatham Offshore and the Common Stock and Senior
         Preferred Stock.

                 (c)      It has adequate means of providing for its current
         needs and possible individual contingencies and is able to bear the
         economic risks of this investment and has a sufficient net worth to
         sustain a loss of its entire investment in Tatham Offshore in the
         event such loss should occur.

                 (d)      It has such knowledge and experience in financial and
         business matters as to be capable of evaluating the merits and risks
         of an investment in Tatham Offshore.


                                           9
<PAGE>   10
                 (e)      It is an "accredited" investor within the meaning of
         "accredited investor" under Regulation D of the Securities Act (as
         amended, "Regulation D").

                 (f)      It is not an issuer or an affiliate thereof, an
         underwriter or dealer.

                 (g)      It understands and agrees that the following
         restrictions and limitations may be applicable to its purchase and
         resales, pledges, hypothecation or other transfers of the Common Stock
         and the Senior Preferred Stock pursuant to any applicable securities
         rule or regulation (which may include Rule 144 or Regulation D and/or
         the regulations promulgated thereunder):

                          (i)     It agrees that the Shares shall not be sold,
                 pledged, hypothecated or otherwise transferred unless it is
                 registered under the Securities Act of 1933 and applicable
                 state securities laws or an exemption from such registration
                 is available; and

                          (ii)    A legend will be placed on any certificate(s)
                 or other document(s) evidencing the investment in
                 substantially the following form:

                          THE SECURITIES REPRESENTED BY THIS INVESTMENT OR
                          DOCUMENT HAVE BEEN ACQUIRED FOR INVESTMENT AND HAVE
                          NOT BEEN REGISTERED UNDER THE SECURITIES ACT OF 1933,
                          AS AMENDED, OR THE SECURITIES LAWS OF ANY STATE.
                          WITHOUT SUCH REGISTRATION, SUCH SECURITIES MAY NOT BE
                          SOLD, PLEDGED, HYPOTHECATED, OR OTHERWISE
                          TRANSFERRED, EXCEPT UPON DELIVERY TO THE CORPORATION
                          OF AN OPINION OF COUNSEL SATISFACTORY TO THE
                          CORPORATION THAT REGISTRATION IS NOT REQUIRED FOR
                          SUCH TRANSFER OR THE SUBMISSION TO THE CORPORATION OF
                          SUCH OTHER EVIDENCE AS MAY BE SATISFACTORY TO THE
                          CORPORATION TO THE EFFECT THAT ANY SUCH TRANSFER
                          SHALL NOT BE IN VIOLATION OF THE SECURITIES ACT OF
                          1933, AS AMENDED, OR APPLICABLE STATE SECURITIES LAWS
                          OR ANY RULE OR REGULATION PROMULGATED THEREUNDER.


                                          10
<PAGE>   11
     4.3         REPRESENTATIONS AND WARRANTIES BY TATHAM OFFSHORE.  Tatham
Offshore warrants to DeepTech as follows:

                 (a)      It is the rightful owner of 100% of the common stock
     of TODI (the "TODI Interest"), free and clear of all liens and
     encumbrances.

                 (b)      The TODI Interest constitutes all of the ownership
     interest in TODI.

                                 ARTICLE V.
                                MISCELLANEOUS

     5.1         ENTIRE AGREEMENT.  This Agreement constitutes the entire
agreement and supersedes all prior (oral or written) or oral contemporaneous
proposals or agreements, all previous negotiations and all other communications
or understandings between the Parties with respect to the subject matter
hereof.

     5.2         AMENDMENT AND MODIFICATION.  All amendments, supplements and
modifications to this Agreement shall be in writing and signed by each of the
Parties.

     5.3         COUNTERPARTS.  This Agreement may be executed in multiple
counterparts, each of which, when executed, shall be deemed an original, and
all of which shall constitute but one and the same instrument.

     5.4         PARTIES BOUND BY AGREEMENT.  This Agreement shall be binding
upon and shall inure to the benefit of the Parties and their respective
successors and assigns.

     5.5         TERMINOLOGY.  All personal pronouns used in this Agreement,
whether used in the masculine, feminine or neuter gender, shall include all
other genders; the singular shall include the plural, and vice versa.  Articles
and other titles or headings are for convenience only, and neither limit nor
amplify the provisions of the Agreement itself, and all references herein to
articles, sections or subdivisions thereof shall refer to the corresponding
article, section or subdivision thereof of this Agreement unless specific
reference is made to such articles, sections or subdivisions of another
document or instrument.

     5.6         LAWS AND REGULATIONS.  This Agreement and all of the terms and
conditions contained herein, and the respective obligations of the Parties, are
subject to all valid and applicable Laws.

     5.7         GOVERNING LAW.  THIS AGREEMENT SHALL BE DEEMED TO BE A
CONTRACT UNDER, AND SHALL BE CONSTRUED, INTERPRETED AND GOVERNED BY AND
ACCORDING TO, THE LAWS OF THE STATE OF TEXAS, EXCLUDING ANY CONFLICT OF LAWS
PRINCIPLES WHICH, IF APPLIED, MIGHT PERMIT OR REQUIRE THE APPLICATION OF THE
LAWS OF ANOTHER JURISDICTION.


                                          11
<PAGE>   12
     5.8         EXHIBITS AND SCHEDULES.  All exhibits, schedules and the like
contained herein or attached hereto are integrally related to this Agreement,
and are hereby incorporated and made a part of this Agreement for all purposes.

     5.9         NOTICES.  Any notice required or permitted to be given under
this Agreement shall be in writing (including telex, facsimile, telecopier or
similar writing) and sent to the address of the Party set forth below, or to
such other more recent address of which the sending Party actually has received
written notice:

         (a)     if to DeepTech, to:

                 DeepTech International Inc.
                 Attn:  President
                 7500 Texas Commerce Tower
                 600 Travis Street
                 Houston, TX  77002

         (b)     if to Tatham Offshore, to:

                 Tatham Offshore, Inc.
                 Attn:  President
                 7400 Texas Commerce Tower
                 600 Travis Street
                 Houston, TX  77002

     Each such notice, demand or other communication shall be effective, if
given by registered or certified mail, return receipt requested, as of the
third day after the date indicated on the mailing certificate, or if given by
any other means, when delivered at the address specified in this Section 5.9.

     5.10        FURTHER ASSURANCES.  Subject to the terms and conditions set
forth in this Agreement, each of the Parties agrees to use all reasonable
efforts to take, or to cause to be taken, all actions, and to do, or to cause
to be done, all things necessary, proper or advisable under applicable laws and
regulations to consummate and make effective the transactions contemplated by
this Agreement.  In case, at any time after the execution of this Agreement, if
any further action is necessary or desirable to carry out its purposes, the
proper officers or directors of the Parties shall take or cause to be taken all
such necessary action.

     5.11        SURVIVAL OF REPRESENTATIONS, WARRANTIES, COVENANTS AND
AGREEMENTS.  The representations, warranties, covenants and agreements given by
the Parties shall survive this Agreement without regard to any action taken
pursuant to this Agreement, including, without limitation, the execution of any
documents affecting an interest in real property or any investigation made by
the Party asserting the breach thereof.


                                          12
<PAGE>   13
     5.12        SEVERABILITY.  Any term or provision of this Agreement that is
invalid or unenforceable in any jurisdiction shall be ineffective as to such
jurisdiction, to the extent of such invalidity or unenforceability, without
rendering invalid or unenforceable the remaining terms and provisions of this
Agreement or affecting the validity or enforceability of any terms and
provisions of this Agreement in any other jurisdiction.  If any provision of
this Agreement is so broad as to be unenforceable, such provision shall be
interpreted to be only so broad as is enforceable.  A bankruptcy or similar
trustee must accept or, to the extent permitted by law, reject this Agreement
in its entirety.

     5.13        ASSIGNMENT.  No Party shall assign any or all of its rights,
interest, title or obligations under this Agreement to any other Person without
the express prior written consent of the other Party, which consent may not be
unreasonably withheld or delayed; provided that, with respect to its rights,
title and interest, either Party shall have the right to (i) make a Transfer to
an Affiliate which remains an Affiliate, (ii) mortgage, pledge, encumber or
otherwise impress a Lien or security interest upon its rights, title and
interest in and to this Agreement, (iii) make a Transfer pursuant to any
security interest arrangement described in (ii) above, including, without
limitation, any judicial or non-judicial foreclosure and any Transfer from the
holder of such security interest to another Person, (iv) make a Transfer in
connection with the sale of all or substantially all of the assets of such
Party, or (v) participate in a merger, consolidation, share exchange,
conversion or other form of statutory reorganization with another Person if
there is a sole surviving Person.  Except for the permitted Transfers described
above, an attempted Transfer made without the prior written consent of the
non-Transferring Party is void ab initio.  Unless otherwise expressly agreed to
in writing by the Parties, a Transferring Party shall continue to be primarily
responsible and liable for all obligations, liabilities and other expenses
arising from or related to this Agreement.

     5.14        WAIVERS.  Neither action taken (including, without limitation,
any investigation by or on behalf of either Party) nor inaction pursuant to
this Agreement, shall be deemed to constitute a waiver of compliance with any
representation, warranty, covenant or agreement contained herein by the Party
not committing such action or inaction.  A waiver by either Party of a
particular right, including, without limitation, breach of any provision of
this Agreement, shall not operate or be construed as a subsequent waiver of
that same right or a waiver of any other right.

     5.15        REMEDIES.  Except as expressly provided herein, the rights,
obligations and remedies created by this Agreement are cumulative and in
addition to any other rights, obligations or remedies otherwise available at
law or in equity. Nothing herein shall be considered an election of remedies.
Without being subject to the limitations required by common law, either Party
may enforce this Agreement by an injunction or specific performance. In
addition, any successful Party is entitled to costs related to enforcing this
Agreement, including, without limitation, attorneys' fees, court costs and
settlement and arbitration expenses.


                                          13
<PAGE>   14
     5.16        NO THIRD PARTY BENEFICIARIES.  Except to the extent a third
party is expressly given rights herein, any agreement herein contained,
expressed or implied, shall be only for the benefit of the Parties and their
respective legal representatives, successors, and assigns, and such agreements
shall not inure to the benefit of any other Person whomsoever, it being the
intention of the Parties that no Person shall be deemed a third party
beneficiary of this Agreement except to the extent a third party is expressly
given rights herein.

     5.17        NO MERGER.  The rights and obligations created by this
Agreement are separate and independent from and in addition to any rights and
obligations created by any other agreements between the Parties, including,
without limitation, the Note Purchase Agreement and the Notes between DeepTech
and Tatham Offshore.  Accordingly, none of the representations, warranties,
covenants or indemnities included in any other agreements between the Parties
shall be merged into this Agreement or otherwise restrict or limit the effect
of this Agreement, but each shall survive as provided in each such agreement.

                    [REMAINDER OF PAGE INTENTIONALLY BLANK]


                                          14
<PAGE>   15

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

                                       DEEPTECH INTERNATIONAL INC.



                                       By:
                                                     -------------------------
                                       Printed Name:
                                                     -------------------------
                                       Title:
                                                     -------------------------




                                       TATHAM OFFSHORE, INC.



                                       By:
                                                     -------------------------
                                       Printed Name:
                                                     -------------------------
                                       Title:
                                                     -------------------------


Exhibit A:       Certificate of Designation of Preferences and Rights of 6%
                 Senior Preferred Stock of Tatham Offshore, Inc.

Exhibit B:       Registration Rights

<PAGE>   16
                                   EXHIBIT A

                         CERTIFICATE OF DESIGNATION OF

                           PREFERENCES AND RIGHTS OF

                           6% SENIOR PREFERRED STOCK

                                       OF

                             TATHAM OFFSHORE, INC.

         TATHAM OFFSHORE, INC., a corporation organized and existing under the
laws of the State of Delaware (the "Company"), does hereby certify that
pursuant to the authority conferred on the Board of Directors of the Company
(the "Board") by the Restated Certificate of Incorporation of the Company (as
amended, the "Certificate of Incorporation") and in accordance with the General
Corporation Law of the State of Delaware (the "DGCL"), at meetings of the Board
held August 20, 1997 and November 13, 1997, the Board adopted the following
resolutions establishing a series of 6,000,000 shares of 6% Senior Preferred
Stock of the Company with the rights, preferences and designations described
below.

                 FURTHER RESOLVED, that pursuant to the authority granted and
         vested in the Board in accordance with the provisions of its
         Certificate of Incorporation, as amended to date, the Board hereby
         creates a class of 6% Senior Preferred Stock, par value $0.01 per
         share (the "6% Senior Preferred Stock");

                 FURTHER RESOLVED, that the designation and amount of the 6%
         Senior Preferred Stock and the voting powers, preferences and
         relative, participating, optional and other special rights of the
         shares of the 6% Senior Preferred Stock, and the qualifications,
         limitations or restrictions thereof, shall be provided for in a
         resolution or resolutions adopted by the Board, pursuant to authority
         expressly vested in it by the provisions of such Certificate of
         Incorporation;

         SECTION 1.  DEFINITIONS.  As used herein, the following terms shall
have the following meanings:

         "Affiliate" means as to any Person, any other Person which, directly
or indirectly, is in control of, is controlled by or is under common control
with such Person.  For the purposes of this definition, the term "control"
means with respect to any Person the power, directly or indirectly, to (i) vote
10% or more of the securities having ordinary voting power for the election of
directors of such Person or (ii) direct or cause the direction of the
management and policies of such Person.  "Controlled" and other derivatives
thereof have a meaning correlative to the foregoing.





                                      A-1
<PAGE>   17
         "Business Combination" means the sale, lease, exchange or transfer of
all or substantially all of the assets of the Company (but specifically
excluding a Farm-Out) for cash, securities or other property to a Person that
is not an Affiliate of the Company or the merger, consolidation or other
business combination of the Company with or into another Person that is not an
Affiliate of the Company.

         "Business Day" means a day which is not a Saturday, Sunday or a day on
which banking institutions are legally authorized to close in the City of New
York.

         "Certificate" means this Certificate of Designation of Preferences and
Rights, as amended, restated or otherwise modified from time to time.

         "Common Stock" means the Company's common stock, $0.01 par value per
share.

         "Default Period" shall have the meaning ascribed to it in Section
6(i).

         "Exchange Warrant" means a warrant that is issued in exchange for
shares of Series A Preferred Stock, Series B Preferred Stock or Series C
Preferred Stock (including all accrued and unpaid dividends thereon) at the
rate of four Exchange Warrants for each share of Series A Preferred Stock,
Series B Preferred Stock or Series C Preferred Stock, and which entitles the
holder thereof to purchase one share of Common Stock at the Trading Reference
Price, subject to adjustment.

         "Junior Dividend Securities" means the Junior Securities (i)
authorized as of the initial date of this Certificate and (ii) any class of
capital stock or series of preferred stock subsequently established by the
Board, the terms of which when established do not expressly provide that such
class or series ranks on parity with or senior to the 6% Senior Preferred Stock
with respect to dividends or distributions.

         "Junior Securities" shall have the meaning ascribed to it in Section 2.

         "Liquidation Preference" means $10.00 per share of 6% Senior Preferred
Stock.

         "Mandatory Redeemable Preferred Stock" means the Mandatory Redeemable
Preferred Stock, $0.01 par value per share, of the Company, each share of which
has a liquidation preference of $0.50 and is mandatorily redeemable by the
Company under certain circumstances and has other rights, preferences and
designations, all as provided in its Certificate of Designation or other
constitutive document, as amended, restated or modified from time to time.

         "Parity Dividend Securities" means Parity Securities authorized as of
the initial date of this Certificate and any class of capital stock or series
of preferred stock established by





                                      A-2
<PAGE>   18
the Board, the terms of which expressly provide that such class or series ranks
on a parity with the 6% Senior Preferred Stock with respect to dividends or
distributions.

         "Parity Securities" shall have the meaning ascribed to it in Section 2.

         "Person" shall mean any individual or any corporation, partnership
(general or limited), joint stock company, business trust, limited liability
company or any other type of entity, organization or association.

         "Record Date" means December 26, 1995.

         "Redemption Date" means any date set by the Board for redeeming all or
a portion of the 6% Senior Preferred Stock pursuant to a redemption under
Section 7.

         "Redemption Price" means $10.00 per share of 6% Senior Preferred
Stock.

         "Senior Dividend Securities" means the Senior Securities authorized as
of the initial date of this Certificate (of which there are none) and any class
of capital stock or series of preferred stock established by the Board, the
terms of which expressly provide that such class or series ranks senior to the
6% Senior Preferred Stock with respect to dividends or distributions.

         "Senior Securities" shall have the meaning set forth in Section 2.

         "Series A Preferred Stock" means the Series A 12% Convertible
Exchangeable Preferred Stock, $0.01 par value per share, of the Company, each
share of which shall accrue dividends at a rate of 12% per annum on the
liquidation preference of $1.50 per share and have other rights, preferences
and designations, all as provided in its Certificate of Designation or other
constitutive document, as amended, restated or modified from time to time.

         "Series B Preferred Stock" means the Series B 8% Convertible
Exchangeable Preferred Stock, $0.01 par value per share, of the Company, each
share of which shall accrue dividends at a rate of 8% per annum on the
liquidation preference of $1.00 per share and have other rights, preferences
and designations, all as provided in its Certificate of Designation or other
constitutive document, as amended, restated or modified from time to time.

         "Series C Preferred Stock" means the Series C 4% Convertible
Exchangeable Preferred Stock, $0.01 par value per share, of the Company, each
share of which shall accrue dividends at a rate of 4% per annum on the
liquidation preference of $0.50 per share and have other rights, preferences
and designations, all as provided in its Certificate of Designation or other
constitutive document, as amended, restated or modified from time to time.





                                      A-3
<PAGE>   19
         "6% Senior Preferred Stock" means the 6% Senior Preferred Stock, $0.01
par value per share, of the Company created by this Certificate, each share of
which shall accrue dividends at a rate of 6% on the Liquidation Preference and
have other rights, preferences and designations, all as provided in this
Certificate.

         "9% Senior Preferred Stock" means the 9% Senior Convertible Preferred
Stock, $0.01 par value per share, of the Company, each share of which shall
accrue dividends at a rate of 9% per annum on the liquidated preference of
$1,000.00 per share and have other rights, preferences and designations, all as
provided in its Certificate of Designation or other constitutive document, as
amended, restated or modified from time to time.

         "Trading Reference Price" means the lowest average of the closing
prices of the Common Stock on the Nasdaq National Market for any five
consecutive trading days during the period commencing on the Record Date and
continuing through and including June 30, 1996 or, if the Common Stock is not
listed on the Nasdaq National Market, the principal stock exchange on which the
Common Stock is then listed or admitted for trading; provided, however, that if
no sales take place on any such day on the Nasdaq National Market or any such
exchange, the closing price shall be deemed to be the average of the last
reported closing bid and asked prices on such day as officially quoted on the
Nasdaq National Market or any such exchange, if such bid and asked prices are
officially quoted, or if the Common Stock is not listed or admitted to trading
on the Nasdaq National Market or any stock exchange, the average of the last
reported closing bid and asked prices on such day in the over-the-counter
market, as furnished by the Nasdaq Stock Market or the National Quotation
Bureau, Inc. or, if neither such entity at the time is engaged in the business
of reporting such prices, as furnished by any similar firm then engaged in such
business.

         Capitalized terms used herein but not otherwise defined in this
Section 1 shall have the meanings ascribed to them throughout this Certificate.
Furthermore, all defined terms contained herein shall be equally applicable to
both singular and plural forms of each such defined term.

         SECTION 2.  DESIGNATION; RANK.  This series of preferred stock shall
be designated "6% Senior Preferred Stock," par value $.01 per share.  The 6%
Senior Preferred Stock will rank, upon liquidation, winding-up and dissolution,
(i) senior to the Common Stock, the 9% Senior Preferred Stock, the Series A
Preferred Stock, the Series B Preferred Stock, the Series C Preferred Stock,
the Mandatory Redeemable Preferred Stock and each other class of capital stock
or series of preferred stock established by the Board the terms of which do not
expressly provide that such class or series ranks on a parity with the 6%
Senior Preferred Stock as to rights upon liquidation, winding-up and
dissolution (collectively referred to as "Junior Securities"); (ii) on a parity
with each other class of capital stock or series of preferred stock established
by the Board the terms of which expressly provide that such class or series
will rank on a parity with the 6% Senior Preferred Stock as to rights upon
liquidation, winding-up and dissolution (collectively referred to as "Parity
Securities"); and (iii) junior to each class of capital stock or series of
preferred stock





                                      A-4
<PAGE>   20
established by the Board the terms of which expressly provide that such class
or series will rank senior to the 6% Senior Preferred Stock (the "Senior
Securities").  As of the date hereof, there are no Parity Securities or Senior
Securities.  With respect to dividends or distributions, the 6% Senior
Preferred Stock will rank (i) senior to the Junior Securities and any other
Junior Dividend Securities; (ii) on parity with the Parity Securities and any
Parity Dividend Securities; and (iii) junior to the Senior Securities and any
Senior Dividend Securities.  The Company will have the right to issue shares of
Junior Securities and Junior Dividend Securities without the approval or
consent of the holders of 6% Senior Preferred Stock.  The Company will not have
the right to issue shares of Senior Securities, Parity Securities, Parity
Dividend Securities or Senior Dividend Securities without the prior consent of
at least a majority-in-interest of the holders of 6% Senior Preferred Stock.

         SECTION 3.  AUTHORIZED NUMBER.  The number of shares constituting the
6% Senior Preferred Stock shall be 6,000,000 shares.

         SECTION 4.  DIVIDENDS.  Holders of shares of the 6% Senior Preferred
Stock will be entitled to receive, when, as and if declared by the Board out of
funds of the Company legally available for payment, cash dividends at an annual
rate of 6% of the Liquidation Preference (or $10.00 per share, subject to
adjustment), payable quarterly in arrears on March 31, June 30, September 30
and December 31 of each year, commencing March 31, 1998.  Each dividend will be
payable to holders of record as they appear on the stock register of the
Company on a record date, not more than 60 nor less than 10 days before the
payment date, fixed by the Board. Dividends will accumulate and be cumulative
from and after the date on which each share of 6% Senior Preferred Stock is
issued. Dividends payable on the 6% Senior Preferred Stock for each full
dividend period will be computed by annualizing the dividend rate and dividing
by four.  Dividends payable for the first dividend period and any period less
than a full dividend period will be computed on the basis of a 360-day year
consisting of twelve 30-day months.  The 6% Senior Preferred Stock will not be
entitled to any dividend, whether payable in cash, property or stock, in excess
of full cumulative dividends.  No interest, or sum of money in lieu of
interest, will be payable in respect of any accrued and unpaid dividends.

         No full dividends may be declared or paid or funds set apart for the
payment of dividends on any securities except for Senior Dividend Securities,
if any, for any period unless full cumulative dividends shall have been paid or
set apart for such payment on the 6% Senior Preferred Stock.  If full dividends
are not so paid, the 6% Senior Preferred Stock shall share dividends pro rata
with the Parity Dividend Securities so that in all cases the amount of
dividends declared per share on the 6% Senior Preferred Stock and Parity
Dividend Securities bear to each other the same ratio that the accumulated
dividends per share on the shares of 6% Senior Preferred Stock and Parity
Dividend Securities bear to each other.  No dividends may be paid or set apart
for such payment on Junior Dividend Securities (except dividends on Junior
Dividend Securities in additional shares of Junior Dividend Securities) and no
Junior Dividend Securities may be repurchased, redeemed or otherwise acquired
nor may funds be set apart for payment with respect thereto, if full dividends
have not been paid on the 6% Senior Preferred Stock. Notwithstanding the





                                      A-5
<PAGE>   21
foregoing, the Company may redeem, purchase or otherwise acquire Junior
Dividend Securities (a) by conversion into, exchange for, or out of the cash
proceeds from the exercise of Exchange Warrants or the substantially concurrent
offering of, Junior Dividend Securities or (b) in the ordinary course of
business pursuant to the terms of any employee stock incentive plan adopted by
the Board.

         SECTION 5.  LIQUIDATION RIGHTS.  In the event of any voluntary or
involuntary liquidation, dissolution or winding up of the Company, before any
payment or distribution of assets is made on any Junior Securities, the holders
of 6% Senior Preferred Stock shall receive an amount equal to the Liquidation
Preference per share plus an amount equal to all accrued and unpaid dividends
thereon through the date of distribution, and the holders of any Parity
Securities shall be entitled to receive an amount equal to the full respective
liquidation preferences (including any premium) to which they are entitled.
If, upon such a voluntary or involuntary liquidation, dissolution or winding up
of the Company, the assets of the Company are insufficient to pay in full the
amounts described above as payable with respect to the 6% Senior Preferred
Stock and any Parity Securities, the holders of the 6% Senior Preferred Stock
and such Parity Securities will share ratably in any such distribution of
assets of the Company first in proportion to their respective liquidation
preference amounts until such amounts are paid in full. After payment of any
such liquidation preference amounts, the shares of 6% Senior Preferred Stock
will not be entitled to any further participation in any distribution of assets
by the Company.  Neither the sale, lease, exchange or transfer of all or
substantially all of the assets of the Company for cash, securities or other
property, nor the merger, consolidation or other business combination of the
Company into or with any other corporation or entity, will be deemed to be a
liquidation, dissolution or winding up of the Company.

         SECTION 6.  LIMITED VOTING RIGHTS.

         Except to the extent as hereinafter expressly provided or as otherwise
required by applicable law, the 6% Senior Preferred Stock shall not have the
right to vote (individually, as a series, class or in the aggregate) on any
matter.

                 (i)      In the event that dividends on the 6% Senior
Preferred Stock, if any, are then declared but not paid as of the relevant
dividend date and remain unpaid in cash for six subsequent quarterly periods,
the maximum authorized number of directors of the Company will be increased as
necessary to allow the holders of 6% Senior Preferred Stock to elect twenty
percent (20%) of the directors on the basis of one vote per each $10.00 amount
of liquidation preference (exclusive of accumulated dividends).  So long as any
shares of 6% Senior Preferred Stock shall be outstanding, the holders of 6%
Senior Preferred Stock shall retain the right to vote and elect such
number/percentage of directors until all dividends on the 6% Senior Preferred
Stock, if any, which are then declared but not paid as of the relevant dividend
date, are paid in full or declared and set aside for payment.  Such period is
hereinafter referred to as a "Default Period".





                                      A-6
<PAGE>   22
                 (ii)     So long as any shares of 6% Senior Preferred Stock
shall be outstanding, during any Default Period, such voting right of the
holders of 6% Senior Preferred Stock may be exercised initially at a special
meeting called pursuant to Section 6(iii) below or at any annual meeting of
stockholders.  The absence of a quorum of holders of Common Stock or any class
thereof shall not affect the exercise of such voting rights by the holders of
6% Senior Preferred Stock.

                 (iii)    Unless the holders of 6% Senior Preferred Stock have,
during an existing Default Period, previously exercised their right to elect
directors, the Board may order, or any stockholder or stockholders owning in
the aggregate not less than 25% of the outstanding shares of 6% Senior
Preferred Stock may request, the calling of a special meeting of holders of 6%
Senior Preferred Stock, which meeting shall thereupon be called by the
President, a Vice President or the Secretary of the Company.  Notice of such
meeting and of any annual meeting at which holders of 6% Senior Preferred Stock
are entitled to vote pursuant to this paragraph shall be given to each holder
of record of 6% Senior Preferred Stock by mailing a copy of such notice to such
holder at such holder's last address as the same appears on the stock register
of the Company. Such meeting shall be called for a time not less than 45 nor
more than 90 days after such order or request.  Notwithstanding the provisions
of this paragraph, no such special meeting shall be called during the period
within 90 days immediately preceding the date fixed for the next annual meeting
of stockholders.

                 (iv)     During any Default Period, the holders of Common
Stock, and other classes of stock of the Company, if applicable, shall continue
to be entitled to elect all of the directors unless and until the holders of 6%
Senior Preferred Stock shall have exercised their right to elect twenty percent
(20%) of the directors voting as a class, after the exercise of which right (1)
the directors so elected by the holders of 6% Senior Preferred Stock shall
continue in office until the earlier of (A) such time as their successors shall
have been elected by such holders or (B) the expiration of the Default Period,
and (2) any vacancy in the Board may be filled by vote of the remaining
directors theretofore elected by the holders of the class of stock which
elected the director whose office shall have become vacant.  References in this
paragraph to directors elected by holders of a particular class of stock shall
include directors elected by such directors to fill vacancies as provided in
clause (2) of the foregoing sentence.

                 (v)      Immediately upon the expiration of a Default Period,
(1) the right of the holders of 6% Senior Preferred Stock to elect directors
shall cease, (2) the term of any directors elected by the holders of 6% Senior
Preferred Stock shall terminate, and (3) subject to immediately preceding
Section 6(iv)(2), the number of directors shall be such number as may be
provided for in the Certificate of Incorporation or bylaws irrespective of any
increase made pursuant to the provisions of Section 6(i) of this section (such
number being subject, however, to change thereafter in any manner provided by
law or in the Certificate of Incorporation or bylaws).





                                      A-7
<PAGE>   23
         SECTION 7.  REDEMPTION.

         (a)     The Company (i) shall redeem outstanding shares of 6% Senior
Preferred Stock at the Redemption Price upon the occurrence of a Business
Combination and (ii) may, but shall have no obligation to, redeem outstanding
shares of 6% Senior Preferred Stock at any time, in each case subject to the
terms set forth below.

         (b)     In connection with a Business Combination, the Company, prior
to the consummation of the Business Combination, shall redeem all outstanding
shares of 6% Senior Preferred Stock; provided, however, that if upon the
Redemption Date the funds of the Company legally available for such redemption
are insufficient to redeem all the shares of 6% Senior Preferred Stock, then
the funds of the Company, to the extent legally available for such purpose,
shall be used to redeem such shares.  If fewer than all the outstanding shares
of 6% Senior Preferred Stock are to be redeemed, the shares of 6% Senior
Preferred Stock to be redeemed shall be determined pro rata as nearly as
practicable, or by such other method as the Board may determine to be fair and
appropriate.  At any time and from time to time thereafter as additional funds
become legally available for the redemption of shares, such funds shall
promptly be used to redeem such additional shares that are required to be
redeemed.

         (c)     Before the Company may optionally redeem any or all of the
outstanding shares of the Junior Securities, the Parity Securities or the
Senior Securities, the Company shall redeem all of the outstanding shares of 6%
Senior Preferred Stock.

         (d)     If fewer than all the outstanding shares of 6% Senior
Preferred Stock are to be redeemed, the shares of 6% Senior Preferred Stock to
be redeemed shall be determined pro rata as nearly as practicable, or by such
other method as the Board may determine to be fair and appropriate.

         (e)     Procedures for Redemption.

                 (i)      In the event the Company shall redeem shares of 6%
         Senior Preferred Stock pursuant to Section 7(a), notice of such
         redemption shall be given by first class mail, postage prepaid, mailed
         not less than 10 days nor more than 60 days prior to the Redemption
         Date, to each holder of record of the shares to be redeemed at such
         holder's address as the same appears on the stock register of the
         Company.  Each such notice shall state:  (i) the Redemption Date; (ii)
         the number of shares of 6% Senior Preferred Stock to be redeemed and,
         if less than all the shares held by such holder are to be redeemed
         from such holder, the number of shares to be redeemed from such
         holder; (iii) the Redemption Price; and (iv) the place or places where
         certificates for such shares are to be surrendered for payment of the
         Redemption Price.  Any notice given in such manner shall be
         conclusively deemed to have been duly given whether or not such notice
         is in fact received.

                 (ii)     Notice having been mailed as aforesaid, from and
         after the Redemption Date (unless the Company shall fail to provide
         money for the payment





                                      A-8
<PAGE>   24
         of the Redemption Price of the shares called for redemption), the
         shares of 6% Senior Preferred Stock so called for redemption shall no
         longer be deemed to be outstanding, and all rights of the holders
         thereof as stockholders of the Company (except the right to receive
         from the Company the Redemption Price) shall cease.  Upon surrender in
         accordance with said notice of the certificates for any shares so
         redeemed (properly endorsed or assigned for transfer, if the Board
         shall so require and the notice shall so state), such shares shall be
         redeemed by the Company at the Redemption Price.  In case fewer than
         all the shares represented by any such certificate are redeemed, a new
         certificate shall be issued representing the unredeemed shares without
         cost to the holder thereof.

         SECTION 8.  NOTICES.  All notices, requests, consents and other
communications hereunder shall be in writing and shall be deemed to have been
made when delivered or mailed first class mail, postage prepaid and addressed
as follows:  (i) in the case of a holder of the 6% Senior Preferred Stock, to
such holder's address as the same appears on the stock register of the Company,
and (ii) in the case of the Company, to the Company's principal executive
offices to the attention of the Company's secretary.

         SECTION 9.  AMENDMENTS AND WAIVERS.  Any right, preference, privilege
or power of, or restriction provided for the benefit of, the 6% Senior
Preferred Stock set forth herein may be amended and the observance thereof may
be waived (either generally or in a particular instance and either
retroactively or prospectively) with the written consent of the Company and the
vote or consent of the holders of at least a majority-in-interest of the shares
of 6% Senior Preferred Stock then outstanding, and any amendment or waiver so
effected shall be binding upon the Company and all holders of the 6% Senior
Preferred Stock.

         SECTION 10.  PREEMPTIVE RIGHTS.  The 6% Senior Preferred Stock is not
entitled to any preemptive rights with respect of any securities of the
Company.

         SECTION 11.  SEVERABILITY OF PROVISIONS.  Whenever possible, each
provision hereof shall be interpreted in a manner as to be effective and valid
under applicable law, but if any provision hereof is held to be prohibited by
or invalid under applicable law, such provision shall be ineffective only the
extent of such prohibition or invalidity, without invalidating or otherwise
adversely affecting the remaining provisions hereof.  If a court of competent
jurisdiction should determine that a provision hereof would be valid or
enforceable if a period of time were extended or shortened or a particular
percentage were increased or decreased, then such court may make such change as
shall be necessary to render the provision in question effective and valid
under applicable law.

                  [REMAINDER OF PAGE INTENTIONALLY LEFT BLANK]





                                      A-9
<PAGE>   25
         IN WITNESS WHEREOF, Tatham Offshore, Inc. has caused this Certificate
of Designation to be duly executed by its duly authorized officer and attested
this [_] day of December, 1997.

                                      TATHAM OFFSHORE, INC.



                                      By:
                                                   -------------------------
                                      Printed Name:
                                                   -------------------------
                                      Title:
                                                   -------------------------

ATTEST:


--------------------------------------------
Printed Name:
                    ------------------------         
Title:
                    ------------------------





                                      A-10
<PAGE>   26
                                   EXHIBIT B
                              REGISTRATION RIGHTS


1.       Demand Registration Rights

         a.      Request for Registration.  For two (2) years after the date on
which the Acquired Stock is issued pursuant to this Agreement, any Holder
owning at least a majority of the shares of the Acquired Stock may make a
written request to Tatham Offshore for registration (the "Demand Registration")
under the Securities Act of the Registrable Securities at any time.  The
Holders shall be entitled to three (3) Demand Registrations with respect to the
Registrable Securities, regardless of the number of shares covered by such
Registration; provided that, if any of the shares that a Holder requested to be
included in a Demand Registration is excluded from such Demand Registration
because of Section 1.(c) of this Exhibit, such Holder shall continue to have
the right to a Demand Registration with respect to such excluded shares.  Any
request for a Demand Registration must specify (i) the number of shares of the
issue of the Registrable Securities proposed to be sold and (ii) the intended
method of disposition thereof.  Within ten days after receipt of such request,
Tatham Offshore shall give written notice of such registration request to all
other Holders of the Registrable Securities, if any, and include in such
registration all Registrable Securities with respect to which Tatham Offshore
has received written requests for inclusion therein within fifteen business
days after the receipt by the applicable Holder of Tatham Offshore's notice.
Each such request will also specify the aggregate number of shares of
Registrable Securities to be registered and the intended method of disposition
thereof.

         b.      Effective Registration and Expenses.  A registration will not
count as a Demand Registration until it has become effective; provided,
however, that if a registration does not become effective solely because of any
act or omission on the part of any Holder, such registration shall nevertheless
count as a Demand Registration.  In any registration initiated as a Demand
Registration, Tatham Offshore will pay all Registration Expenses in connection
therewith.

         c.      Priority on Demand Registrations.  If the Holders of at least
a majority of shares of an issue of Registrable Securities to be registered in
a Demand Registration so elect, the offering of such issue of Registrable
Securities shall be in the form of an underwritten offering.  In such event, if
the managing underwriter or underwriters of such offering advise Tatham
Offshore and the Holders in writing that, in their opinion, the aggregate
amount of Registrable Securities requested to be included in such offering will
materially and adversely affect the success or offering price of such offering,
Tatham Offshore will include in such registration the aggregate amount of such
Registrable Securities which, in the opinion of such managing underwriter or
underwriters, can be sold without any such material adverse effect.  Such
securities would then be allocated pro rata among the Holders on the basis of
the number of Registrable Securities requested to be included in such
registration by their Holders.





                                      B-1
<PAGE>   27
         d.      Selection of Underwriters.  If any Demand Registration is in
the form of an underwritten offering, Tatham Offshore will select and obtain
the investment banker or investment bankers and manager or managers that will
administer the offering; provided that such investment bankers and managers
must be reasonably satisfactory to the DeepTech Holder or, if there is no
DeepTech Holder, a majority-in-interest of the Holders.

2.       Piggyback Registration.

         For two (2) years after the date on which the Acquired Stock is
issued, if Tatham Offshore at any time proposes to file on its behalf and/or on
behalf of any of its security holders (the "Registered Security Holders") a
registration statement under the Securities Act on any form (other than a
registration statement on Form S-4 or S-8 or any similar or successor form or
any other registration statement relating to an exchange offer or offering of
securities solely to Tatham Offshore's existing security holders or employees),
it will give written notice to each Holder at least twenty (20) days before the
anticipated date of initial filing with the Commission of such registration
statement, which notice shall set forth Tatham Offshore's intention to effect
such a registration, the class or series and number of equity securities
proposed to be registered and the intended method of disposition of the
securities proposed to be registered by Tatham Offshore.  The notice shall
offer to include in such filing the aggregate number of shares of Acquired
Stock as such Holder may request.  Nothing in this Section 2 shall preclude
Tatham Offshore from discontinuing the registration of its securities being
effected on its behalf under this Section 2 at any time prior to the effective
date of the registration relating thereto.

3.       Registration Procedures

         a.      For Demand Registration.

                 Tatham Offshore will use commercially reasonable efforts to
         effect a Demand Registration requested by a Holder in accordance with
         the intended method of disposition thereof as quickly as practicable.
         Such efforts by Tatham Offshore shall include:

                 (i)      preparing and filing with the Commission, not later
         than 60 days after receipt of a request to file a Demand Registration,
         a registration statement on any form that is available for the sale of
         such issue of Registrable Securities by Tatham Offshore in accordance
         with the intended method of distribution thereof and using
         commercially reasonable efforts to cause such registration statement
         to become effective reasonably promptly thereafter;





                                      B-2
<PAGE>   28
                 (ii)     preparing and filing with the Commission any
         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 which will terminate when all Registrable
         Securities covered by such registration statement have been sold (but
         not before the expiration of the 90-day 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 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)    as soon as reasonably practicable, furnishing to each
         seller of Registrable Securities to be included in the Demand
         Registration copies of such registration statement as filed and each
         amendment and supplement 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 such seller;

                 (iv)     using commercially reasonable efforts to register or
         qualify such Registrable Securities under such other securities or
         blue sky laws of such appropriate jurisdictions and do any and all
         other acts and things which may be reasonably necessary to enable such
         seller to consummate the disposition of the Registrable Securities
         owned by such seller in such jurisdictions; provided that Tatham
         Offshore will not be required to (i) qualify generally to do business
         in any jurisdiction where it would not otherwise be required to
         qualify but for this paragraph (d), (ii) subject itself to taxation in
         any such jurisdiction or (iii) consent to general service of process
         in any such jurisdiction;

                 (v)      using commercially 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 Tatham Offshore to enable the seller or sellers thereof
         to consummate the disposition of such Registrable Securities;

                 (vi)     making available for inspection by any underwriter
         participating in any disposition pursuant to such registration
         statement, and any attorney, accountant or other agent retained by any
         such underwriter (collectively, the "Inspectors"), all financial and
         other records, pertinent corporate documents and properties of Tatham
         Offshore (collectively, the "Records"), and cause Tatham Offshore's
         officers, directors and employees to supply all information reasonably
         requested by any such Inspector, as shall be reasonably necessary to
         enable them to exercise their due diligence responsibility, in
         connection with such registration statement.  Records or other
         information which Tatham Offshore has determined,





                                      B-3
<PAGE>   29
         in good faith, to be confidential and which they notify the Inspectors
         are confidential shall not be disclosed by the Inspectors unless (i)
         the disclosure of such Records or other information is required to be
         disclosed pursuant to the Securities Act or is necessary to avoid or
         correct a misstatement or omission in the registration statement or
         (ii) the release of such Records or other information is ordered
         pursuant to a subpoena or other order from a court of competent
         jurisdiction.  Upon learning that disclosure of such Records or other
         information is sought in a court of competent jurisdiction, the Holder
         (including its transferees) agrees that it will give notice to Tatham
         Offshore and allow Tatham Offshore to undertake appropriate action to
         prevent disclosure of the Records or other information deemed
         confidential; and

                 (vii)    if required by applicable listing requirements, cause
         all such Registrable Securities to be listed on each securities
         exchange on which similar securities issued by Tatham Offshore are
         then listed, provided that the applicable listing requirements are
         satisfied.

                 Tatham Offshore may require each seller of Registrable
         Securities under a Demand Registration to furnish to Tatham Offshore
         information regarding the distribution of such securities as Tatham
         Offshore may from time to time request.

         b.      For Piggyback Registration.

                 If the Holder desires to have the Acquired Stock registered
         under Section 2 of this Exhibit, such Holder shall advise Tatham
         Offshore in writing within fifteen (15) days after the date of receipt
         of such offer from Tatham Offshore, setting forth the amount of the
         Acquired Stock for which registration is requested.  Tatham Offshore
         shall thereupon include in such filing the number of shares of the
         Acquired Stock for which registration is so requested, subject to the
         next sentence, and shall use its best efforts to effect registration
         of such Acquired Stock under the Securities Act.  If the managing
         underwriter of a proposed public offering shall advise Tatham Offshore
         in writing that, in its opinion, the distribution of the Acquired
         Stock requested to be included in the registration concurrently with
         the securities being registered by Tatham Offshore or any Registered
         Security Holder would materially and adversely affect the distribution
         of such securities by Tatham Offshore or such Registered Security
         Holders, then the Holder and the Registered Security Holders shall
         reduce the number of securities intended to be distributed through
         such offering on a pro rata basis.

4.       Registration Expenses

         All expenses incident to Tatham Offshore's performance of or
compliance with this Agreement, including without limitation, all registration
and filing fees, fees and expenses of compliance with securities or blue sky
laws (including fees and





                                      B-4
<PAGE>   30
disbursements of counsel in connection with blue sky qualifications of the
Registrable Securities), rating agency fees, printing expenses, messenger and
delivery expenses, internal expenses (including, without limitation, all
salaries and expenses of its officers and employees performing legal or
accounting duties), the fees and expenses incurred in connection with the
listing of the securities to be registered on each securities exchange on which
similar securities issued by Tatham Offshore are then listed, and fees and
disbursements of counsel for Tatham Offshore and its independent certified
public accountants, securities acts liability insurance (if Tatham Offshore
elects to obtain such insurance), and the fees and expenses of any special
experts retained by Tatham Offshore in connection with such registration, fees
and expenses of other persons retained by Tatham Offshore (but not including
any underwriting discounts or commissions or transfer taxes attributable to the
sale of Registrable Securities) will be borne by Tatham Offshore (all such
expenses referred to herein as the "Registration Expenses").

5.       Indemnification; Contribution

         a.      Indemnification by Tatham Offshore.  Tatham Offshore agrees to
indemnify, to the fullest extent permitted by law, each Holder, the
underwriters and each of their respective officers, directors and agents and
each person who controls such Holder (within the meaning of the Securities Act)
against all losses, claims, damages, liabilities and expenses caused by any
untrue or alleged untrue statement of material fact contained in any
registration statement, prospectus or preliminary prospectus 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 case of a prospectus or
preliminary prospectus, in the light of the circumstances under which they were
made) not misleading, except insofar as the same are caused by or contained in
any information with respect to such Holder furnished in writing to Tatham
Offshore by such Holder expressly for use therein.

         b.      Indemnification by Holder of Registrable Securities.  In
connection with any Demand Registration in which a Holder is participating,
each such Holder will furnish to Tatham Offshore in writing such information
with respect to such Holder as Tatham Offshore reasonably requests for use in
connection with any such registration statement or prospectus and agrees to
indemnify, to the extent permitted by law, Tatham Offshore, the underwriters
and each of their respective directors and officers and each person who
controls Tatham Offshore (within the meaning of the Securities Act) against any
losses, claims, damages, liabilities and expenses resulting from any untrue or
alleged untrue statement of a material fact or any omission or alleged omission
of a material fact required to be stated in the registration statement,
prospectus or preliminary prospectus or any amendment thereof or supplement
thereto or necessary to make the statements therein (in the case of a
prospectus or preliminary prospectus, in the light of the circumstances under
which they were made) not misleading, to the extent, but only to the extent,
that such untrue statement or omission is contained in any information with
respect to such Holder so furnished in writing by such Holder; provided that no
Holder in any event shall be liable for any amount in excess of the net
proceeds received from such Holder's sale of its shares of Acquired Stock.





                                      B-5
<PAGE>   31
         c.      Conduct of Indemnification Proceedings.  Any person entitled
to indemnification hereunder agrees to give prompt written notice to the
indemnifying party after the receipt by such person of any written notice of the
commencement of any action, suit, proceeding or investigation or threat thereof
made in writing for which such person will claim indemnification or
contribution pursuant to this Agreement and, unless in the reasonable judgment
of such indemnified party a conflict of interest may exist between such
indemnified party and the indemnifying party with respect to such claim, permit
the indemnifying party to assume the defense of such claim with counsel
reasonably satisfactory to such indemnified party.  Whether or not such defense
is assumed by the indemnifying party, the indemnifying party will not be
subject to any liability for any settlement made without its consent (but such
consent will not be unreasonably withheld). No indemnifying party will consent
to entry of any judgment or enter into any settlement which does not include as
an unconditional term thereof the giving by the claimant or plaintiff to such
indemnified party of a release from all liability in respect of such claim or
litigation.  If the indemnifying party is not entitled to, or elects not to,
assume the defense of a claim, it will not be obligated to pay the fees and
expenses of more than one counsel with respect to such claim, unless in the
reasonable judgment of any indemnified party a conflict of interest may exist
between such indemnified party and any other of such indemnified parties with
respect to such claim, in which event the indemnifying party shall be obligated
to pay the fees and expenses of such additional counsel or counsels.

6.       Participation in Underwritten Registrations

         No Holder may participate in any underwritten registration hereunder
unless such Holder (a) agrees to sell such Holder's securities on the basis
provided in any underwriting arrangements approved by the persons entitled
hereunder to approve such arrangements and (b) completes and executes all
questionnaires, powers of attorney, indemnities, underwriting agreements and
other documents reasonably required under the terms of such underwriting
arrangements.

7.       Rule 144

         Tatham Offshore covenants that (i) it will file the reports required
to be filed by it under the Securities Act and the Exchange Act and the rules
and regulations adopted by the Commission thereunder and (ii) take such further
action as any Holder may reasonably request, all to the extent required from
time to time to enable such Holder to sell Registrable Securities without
registration under the Securities Act within the limitation of the exemptions
provided by (a) Rule 144 under the Securities Act, as such Rule may be amended
from time to time, or (b) any similar rule or regulation hereafter adopted by
the Commission.





                                      B-6