Exhibit 10.2

HORIZON OFFSHORE, INC.
2500 CityWest Boulevard, Suite 2200
Houston, Texas 77042

March 31, 2005

The Holders of Subordinated Notes Signatory Hereto

Ladies and Gentlemen:

     Reference is made to the Financing Agreement (the “Financing Agreement”)
dated as of March 31, 2005 among Horizon Offshore, Inc. (the “Company”), each of
its subsidiaries party thereto, Manchester Securities Corp., as collateral and
administrative agent (“Manchester”), and the other lenders specified therein
(collectively, the “Senior Lenders”), whereby, subject to satisfaction of all
conditions precedent set forth therein, the Senior Lenders propose to extend
credit in the form of a $70 million senior secured financing facility (the “New
Credit Facility”). By your execution of a counterpart of this letter agreement,
you acknowledge receipt of a copy of the Financing Agreement. Capitalized terms
used and not otherwise defined herein are used with the meanings ascribed
thereto in the Financing Agreement.

     The Company and each holder of Subordinated Notes signatory hereto (the
“Investors”), in consideration of the mutual agreements and covenants of the
parties hereto and the Company’s agreement to issue to the Investors the Recap
Common Stock and the New Preferred Stock (as such terms are defined below),
hereby agree as follows:

     1. Upon the consummation of the Recap (as defined in paragraph 3 below),
you agree that without the need for any further act or evidence, the
Subordinated Notes and the Subordinated Note Debt Documents are and shall be
deemed amended effective as of the Recap Closing Date (as defined in paragraph 4
below) to (i) reduce the interest rate to 8% per annum; (ii) extend the maturity
date to March 31, 2010; and (iii) delete the provisions of the Subordinated Note
Debt Documents and events of default specified in Schedule II attached hereto.
You agree to take such action and deliver, or cause to be delivered, such
agreements, instruments or other documents as the Company and Manchester may
reasonably request in order to reflect the amendments and release contemplated
by paragraphs 1 and 2 hereof.

     2. You consent to all transactions contemplated by this letter, the
Financing Agreement and the other Loan Documents, and agree that the Obligations
to be incurred thereunder shall constitute “Refinancing Indebtedness” as that
term is defined and used in the Subordinated Note Debt Documents, and you
further consent to the assignment to, or releases in favor of, Manchester, as
Collateral Agent for the Senior Lenders of all of your rights to the collateral
securing the Subordinated Note Debt you hold and the proceeds of such
collateral, and you consent to the execution by Elliott Associates, L.P., as
collateral agent for the Holders (as defined in the Subordinated Note Debt
Documents), of any assignments or releases of security interests and liens
existing for your benefit with respect to such collateral (including
authorization to file UCC-3 assignment and/or termination statements) and the
return to the Company of any cash or other collateral or proceeds thereof held
by Elliott Associates, L.P., as such collateral agent.

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     3. The Company will use its best efforts to consummate a series of
recapitalization transactions (collectively, the “Recap”) promptly following the
funding of the Loans pursuant to which $84,972,823 in aggregate principal amount
of Subordinated Notes, representing the aggregate principal amount thereof as of
March 31, 2005, and all accrued and unpaid interest for any period after such
date prior to the Recap (such that only $25,000,000 aggregate principal amount
of Subordinated Notes would remain outstanding, modified as described above) and
all 1,400 shares of the Company’s Series A Redeemable Participating Preferred
Stock (“Series A Preferred Stock”) would be exchanged for a portion of a new
series of one million shares of a convertible preferred stock of the Company
(“New Preferred Stock”) and a portion of 60 million newly issued shares of the
Company’s common stock (the “Recap Common Stock”). The conversion rate under the
New Preferred Stock will be set such that the total outstanding Recap Common
Stock and the New Preferred Stock, on an “as converted” basis, will represent in
the aggregate 95% of the Company’s common stock on a fully diluted basis (which
calculation excludes out-of-the-money director and employee stock options), pro
forma for the Recap and the other transactions described herein. The Recap
Common Stock and the New Preferred Stock shall also be deemed issued to you by
the Company as an inducement to, and as additional consideration for, your
agreements to amend the Subordinated Notes and Subordinated Debt Documents set
forth in paragraph 1; your consents set forth in paragraph 2; and, if
applicable, your commitment to and/or participation in the New Credit Facility
as a Senior Lender.

     4. The New Preferred Stock will be issued immediately prior to the issuance
of the Recap Common Stock, and will carry an aggregate liquidation preference
equal to the greater of (i) $40,000,000 and (ii) the amount the New Preferred
Stock would receive on an “as converted” basis (as if the amendment to the
Company’s certificate of incorporation referred to below had been adopted). The
New Preferred Stock will not entitle holders to any dividend or voting rights
(except as required by the Delaware General Corporation Law (the “DGCL”)), will
be mandatorily convertible upon amendment to the Company’s certificate of
incorporation to increase the number of authorized shares of common stock to
accommodate the conversion and to reduce or eliminate any par value for the
common shares as deemed necessary or appropriate by the Company and Manchester
in connection therewith (but in no event will such mandatory conversion occur
prior to six months and one day after the date of initial issuance). The
Certificate of Designation, Preferences and Rights of the New Preferred Stock
will be substantially in the form of Exhibit A attached hereto. The New
Preferred Stock and the Recap Common Stock will be earned (subject to
performance by each Investor at the Recap Closing Date as contemplated herein)
at the time of funding of the Loans (the “Equity Earned Date”) (with the New
Preferred Stock being deemed earned immediately prior to the earning of the
Recap Common Stock), and will be issued as promptly as possible following the
Equity Earned Date upon consummation of the Recap in accordance with paragraph 3
(the “Recap Closing Date”) after the Company completes the voluntary de-listing
of its common stock from the Nasdaq Stock Market and expiration of the waiting
period under the Hart-Scott-Rodino Antitrust Improvements Act of 1976 if a
filing thereunder is determined to be required by the Company and any Investor
in connection with the Recap. If any such filing is determined to be required
and is applicable to you, you agree to prepare and make such filing although the
Company will reimburse you for your expenses and any filing fee incurred in
connection therewith.

     5. The Company will call a meeting of shareholders to be held not earlier
than September 15, 2005 nor later than October 31, 2005, to accomplish the
amendments to the

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Company’s certificate of incorporation described above, and an amendment to
delete the prohibition of action by stockholder consent in lieu of a meeting.
You agree to participate in the Recap on a pro rata basis (based upon the
aggregate principal amount of Subordinated Notes you hold relative to the
aggregate principal amount of all such notes) and to exercise any voting power
you may have to approve the amendments to the Company’s certificate of
incorporation described above, and to execute such documentation and take such
other action as may reasonably be required in connection therewith.

     6. Certain Investors by their execution hereof have agreed to participate
in the New Credit Facility as Senior Lenders, and Schedule I hereto sets forth
the Term Loan A Commitment and Term Loan B Commitment of each such Senior Lender
and Manchester. Schedule I hereto also sets forth for each Investor the number
of shares of Recap Common Stock and New Preferred Stock to be received by it as
aggregate consideration for the actions to be taken by such Investor reflected
in this Agreement (including the commitment to finance). All such shares shall
be earned as of the Equity Earned Date, as provided in paragraph 4, and all such
shares of New Preferred Stock will be issued in a single transaction on the
Recap Closing Date, and all such shares of Recap Common Stock will be issued in
a single transaction immediately thereafter.

     7. At the Recap Closing Date, the Company will execute with Manchester, the
Senior Lenders and each of you a registration rights agreement in customary form
providing for demand, piggyback and resale shelf registration rights concerning
(i) the shares of common stock received or receivable by Manchester, each Senior
Lender and each of you as a result of the Recap (including upon conversion of
New Preferred Stock) and (ii) the Subordinated Notes which remain outstanding
after the Recap Closing Date. Such agreement will, among other things,
(x) require the Company to file a resale shelf registration statement within
90 days of the Recap Closing Date, to use its best efforts to secure the
effectiveness thereof at the earliest possible date, and to maintain such
effectiveness at all times thereafter (subject to customary suspension period
provisions), and (y) contain customary indemnification and expense reimbursement
provisions for your benefit.

     8. You agree that the letter agreement dated October 28, 2004 (effective
November 4, 2004) among the Company and the investors party thereto is
superseded by this letter and that upon the occurrence of the Equity Earned
Date, such agreement shall be of no further effect, except for paragraph 7
thereof, which shall survive such termination.

     9. The Company represents that at the date hereof there are 32,252,658
shares of common stock outstanding and that except for out-of-the money stock
options (which do not contain anti-dilution provisions which would be triggered
by the Recap) and the Series A Preferred Stock there are no other equity
securities outstanding. You represent that the number of shares of the Company’s
common stock specified beneath your signature hereto is a true and correct
representation of all of the Company’s common stock of which you are a
beneficial owner (within the meaning of Rule 16a-1(a)(1) promulgated under the
Securities Exchange Act of 1934) as of the date hereof. You further represent
that the aggregate original principal amount of each issuance of the Company’s
Subordinated Notes that you hold is specified beneath your signature hereto;
that such notes are held by you free of any liens or encumbrances; and that you
have full authority to execute this letter agreement and to consummate all of
the Proposed

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Transactions (as defined below in paragraph 11) as it pertains to you without
the requirement of obtaining the consent or authorization of any other person,
entity or governmental authority except for any requirements of the
Hart-Scott-Rodino Antitrust Improvements Act of 1976, if applicable to you. You
agree that, except for sales of common stock pursuant to the resale shelf
registration statement contemplated by paragraph 7 hereof (but in no event
earlier than the later of (x) the date which is six months and one day following
the Recap Closing Date and (y) the automatic conversion of the New Preferred
Stock), you will not sell, transfer, pledge or otherwise dispose of any
Subordinated Notes you own or any shares of Recap Common Stock or New Preferred
Stock you acquire on the Recap Closing Date (each, a “Transfer”) unless you
(i) provide at least 10 business days’ prior written notice of such proposed
Transfer to the Company, (ii) secure an agreement in writing from the proposed
Transferee to adopt, ratify and agree to be bound by and perform this letter
agreement as if it were a signatory hereto and furnish the Company with a fully
executed counterpart thereof prior to completing such Transfer, which agreement
shall expressly name the Company and the other Investors as third party
beneficiaries with the right to enforce the Transferee’s obligations thereunder
and hereunder, and (iii) otherwise comply with any applicable requirements
governing Transfers of Subordinated Notes set forth in the applicable
Subordinated Note Debt Documents under which such notes were issued, and
applicable requirements of laws governing the Transfer of unregistered
securities. You agree that the certificates evidencing New Preferred Stock and
Recap Common Stock to be issued to you will bear a legend setting for the
Transfer restrictions, voting obligations and the other agreements set forth
herein.

     10. Notwithstanding any term to the contrary contained in this letter
agreement, the agreements and covenants of the Investors set forth herein are
conditioned upon the occurrence of the Equity Earned Date not later than
March 31, 2005.

     11. The Company agrees to, and will cause each of its subsidiaries to,
indemnify, defend and hold harmless each Investor, each partner, member,
shareholder and affiliate of each Investor and each of its and their respective
representatives (each, an “Indemnified Party”) from and against any and all
claims, actions, damages, losses, liabilities, costs and expenses (including,
without limitation, fees and disbursements of counsel), that may be incurred by,
asserted or awarded against or imposed upon any Indemnified Party, in each case
arising out of or in connection with or relating to any investigation,
litigation or proceeding or the preparation of any defense with respect thereto,
arising out of or in connection with or relating to this letter agreement, the
Recap, the New Credit Facility or any other transaction or action described
herein (collectively, the “Proposed Transactions”), whether or not such
investigation, litigation or proceeding is brought by the Company, any of its
subsidiaries, shareholders or creditors, an Indemnified Party or any other
person, or an Indemnified Party is otherwise a party thereto and whether or not
the Proposed Transactions are consummated, except to the extent such claim,
action, damage, loss, liability, cost or expense is found in a final
non-appealable judgment by a court of competent jurisdiction to have resulted
from such Indemnified Party’s gross negligence or willful misconduct. IT IS THE
INTENT OF THE PARTIES HERETO THAT EACH INDEMNIFIED PARTY BE INDEMNIFIED FOR ITS
ORDINARY, SOLE OR CONTRIBUTORY NEGLIGENCE. The Company further agrees that no
Indemnified Party shall have any liability (whether direct or indirect, in
contract, tort or otherwise) to the Company or any of its subsidiaries,
shareholders or creditors for or in connection with this letter agreement or the
Proposed Transactions or other actions contemplated hereby, except to the extent
such

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liability is expressly set forth in a definitive agreement to which such
Indemnified Party is bound or is found in a final non-appealable judgment by a
court of competent jurisdiction to have resulted from such Indemnified Party’s
gross negligence or willful misconduct. In no event, however, shall any
Indemnified Party be liable on any theory of liability for any special,
indirect, consequential or punitive damages. In connection with the foregoing
obligation to indemnify, defend and hold harmless the Indemnified Parties, the
Company agrees that, in the event of anticipated, threatened or actual
litigation, it shall, upon demand of an Indemnified Party who determines that it
is or is likely to be a party to such anticipated, threatened or actual
litigation, advance a reasonable amount of monies relative to such anticipated,
threatened or actual litigation in order to fulfill the obligation to defend
such Indemnified Party against any and all losses, claims, damages, expenses and
liabilities to which such Indemnified Party may become subject in connection
with the transactions described herein or the financing contemplated hereby.

     12. (a) From and after the Recap Closing Date, the Company will and you
acknowledge that the Company will (and you will not, directly or indirectly,
oppose or object to actions taken by the Company to), indemnify and hold
harmless each present director and officer of the Company and its Subsidiaries
(the “Indemnified Company Parties”), against any costs or expenses (including
attorneys’ fees), judgments, fines, losses, claims, damages, liabilities or
amounts paid in settlement (collectively, “Costs”) incurred in connection with
any claim, action, suit, proceeding or investigation, whether civil, criminal,
administrative or investigative, arising out of or pertaining to any act or
omission in their capacity as a director or officer occurring on or prior to the
Recap Closing Date (including for acts or omissions in connection with the
approval of this letter agreement and the consummation of the transactions
contemplated hereby), whether asserted or claimed prior to, at or after the
Recap Closing Date, to the fullest extent permitted under applicable law (and
the Company shall also advance reasonable expenses as incurred to the fullest
extent permitted under applicable law; provided that, if required by applicable
law, the Indemnified Company Party to whom expenses are advanced provides an
undertaking to repay such advances if it is ultimately determined that such
Indemnified Party is not entitled to indemnification). For four years from the
Recap Closing Date, the Company will, and you acknowledge that the Company will
(and you will not, directly or indirectly, oppose or object to any actions taken
by the Company to) maintain in effect for the benefit of the Company’s current
directors and officers an insurance and indemnification policy that provides
coverage for acts or omissions occurring prior to the Recap Closing Date (the
“D&O Insurance”) covering each such person currently covered by the officers’
and directors’ liability insurance policies of the Company on terms with respect
to coverage and in amounts no less favorable than those of the Company’s
policies in effect on the date hereof with the same or comparable quality
insurance carriers; provided, however, that the Company shall not be required to
pay an annual premium for the D&O Insurance in excess of 200% of the premium for
the 2004 fiscal year (the “Maximum Premium”); provided, further, however, if
such D&O Insurance coverage cannot be obtained at all, or can only be obtained
at an annual premium in excess of the Maximum Premium, the Company shall obtain
the most advantageous policies of directors’ and officers’ insurance obtainable
for an annual premium equal to the Maximum Premium. The provisions of this
paragraph 12 are intended to be in addition to the rights otherwise available to
the current and former officers and directors of the Company by applicable law,
charter, by-law or agreement. You acknowledge that the Company will (and you
will not, directly or indirectly, oppose or object to actions taken by the
Company to) keep in

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effect after the Recap Closing Date provisions in its certificate of
incorporation and bylaws providing for exculpation of director and officer
liability and its indemnification of the Indemnified Company Parties to the
fullest extent permitted under the DGCL, which provisions will not be amended
except as required by applicable law or except to make changes permitted by law
that would enlarge the Indemnified Company Parties’ right of indemnification.
You acknowledge that the Company will (and you will not, directly or indirectly,
oppose or object to actions taken by the Company to) honor any of the
indemnification agreements entered into with its directors and keep in effect
after the Recap Closing Date all of the provisions in its certificate of
incorporation and bylaws providing for exculpation of director and officer
liability and its indemnification of the Indemnified Company Parties to the
fullest extent permitted under the DGCL, which provisions will not be amended
except as required by applicable law or except to make changes permitted by law
that would enlarge the “Indemnified Company Parties” right of indemnification.

     (b) In the event that the Company or its successors or assigns
(i) consolidates with or merges into any other person and is not the continuing
or surviving corporation or entity of such consolidation or merger or
(ii) transfers or conveys all or substantially all its properties and assets to
any person, then, and in each such case, the Company shall, as a condition
precedent to any such transaction, cause proper provisions to be made so that
the successors and assigns of the Company assume the obligations set forth in
this paragraph 12. The obligations of the Company under this paragraph 12 shall
not be terminated or modified in such a manner as to adversely affect any
indemnitee to whom this paragraph 12 applies without the express written consent
of such affected indemnitee (it being expressly agreed that the indemnitees to
whom this paragraph 12 applies shall be third party beneficiaries of this
paragraph 12).

     13. Except as provided in paragraph 12(b), this letter agreement may not be
amended or waived except by an instrument in writing signed by the Company and
each Investor. This letter agreement may be executed in any number of
counterparts, no one of which need be signed by all parties but each of which
shall be an original, and all of which, when taken together, shall constitute
one agreement. Delivery of an executed signature page of this letter agreement
by facsimile transmission shall be effective as delivery of a manually executed
counterpart hereof. This letter agreement will become effective upon execution
of a counterpart hereof by each Investor.

     14. Each of the Investors hereby represents and warrants that in making its
decision to enter into this letter agreement, to undertake the obligations to
performed by it hereunder and to participate in the Recap, it has independently,
and without reliance upon Manchester or any of its affiliates, and based on such
information as such Investor has deemed appropriate, made its own investment and
credit analyses and decision to enter into this letter agreement.

     15. The Company and each Investor hereby irrevocably waives all right to
trial by jury in any action, proceeding or counterclaim (whether based on
contract, tort or otherwise) arising out of or relating to this letter agreement
or the Proposed Transactions or the actions of the Company, any Investor or any
of its respective representatives in the negotiation, performance or enforcement
hereof.

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     16. You acknowledge and agree that Manchester and its affiliates are
intended third party beneficiaries under this letter agreement.

     17. This letter agreement shall be construed in accordance with, and this
letter agreement and all matters arising out of or relating in any way
whatsoever to it (whether in contract, tort or otherwise) shall be governed by
the laws of the State of New York.

[Signature pages to follow]

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     Please confirm that the foregoing is our mutual understanding by signing
and returning to the Company an executed counterpart of this letter agreement.

              Very truly yours,
 
            HORIZON OFFSHORE, INC.
 
       

  By:    

     

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           Name:

           Title:

[Recapitalization Letter]

 

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                  ELLIOTT ASSOCIATES, L.P.    
 
                By:   Elliott Capital Advisors, L.P.,
as General Partner
 
           

  By:   Braxton Associates, Inc.,
as General Partner    
 
           

  By:                

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           Name:    

           Title:    
 
                Address: 712 Fifth Avenue                     36th Floor        
        New York, New York 10019
 
                Common Stock Beneficially Owned:   0 Shares
 
                16% Subordinated Notes Held         (Original Principal Amount):
  $6,186,276.66
 
                18% Subordinated Notes Held         (Original Principal Amount):
  $3,526,057.58
 
                ELLIOTT INTERNATIONAL, L.P.    
 
                By:   Elliott International Capital Advisors Inc.,
as Attorney-in-Fact
 
           

  By:                

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           Name:    

           Title:    
 
                Address: 712 Fifth Avenue                     36th Floor        
        New York, New York 10019
 
                Common Stock Beneficially Owned:   0 Shares
 
                16% Subordinated Notes Held         (Original Principal Amount):
  $12,372,553.35
 
                18% Subordinated Notes Held         (Original Principal Amount):
  $  5,289,086.17

[Recapitalization Letter]

 

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                  FALCON MEZZANINE PARTNERS, LP
 
                By:   Falcon Mezzanine Investments, LLC, its
General Partner
 
           

  By:                

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           Name:    

           Title:    
 
                Address: 60 Kendrick Street                     Needham,
Massachusetts 02494                 Telecopier No.: (781) 247-7299
 
                Common Stock Beneficially Owned:   0 Shares
 
                16% Subordinated Notes Held         (Original Principal Amount):
  $22,085,007.68
 
                18% Subordinated Notes Held         (Original Principal Amount):
  $  7,051,464.97

[Recapitalization Letter]

 

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                  D. E. SHAW LAMINAR PORTFOLIOS, L.L.C.
 
           

  By:                

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           Name:    

           Title:    
 
                Address: 120 West 45th St.                     New York, New
York 10036
 
                Common Stock Beneficially Owned:   0 Shares
 
                16% Subordinated Notes Held         (Original Principal Amount):
  $3,897,354.30
 
                18% Subordinated Notes Held         (Original Principal Amount):
  $   766,648.36

[Recapitalization Letter]

 

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                  LANGLEY PARTNERS, L.P.    
 
                By:   Langley Capital, LLC,
as General Partner
 
           

  By:                

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               Name: Jeffrey Thorp              Title: Managing Member
 
                Address: 535 Madison Avenue, 7th Floor                     New
York, New York 10022
 
                Common Stock Beneficially Owned:   103,100 Shares
 
                16% Subordinated Notes Held         (Original Principal Amount):
  $1,239,714.43
 
                18% Subordinated Notes Held         (Original Principal Amount):
  $                   0

[Recapitalization Letter]

 

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                  SACC PARTNERS, LP    
 
           

  By:                

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               Name: Tom Kelleher              Title: General Partner
 
                Address: 11150 Santa Monica Blvd., Suite 750            
        Los Angeles, CA 90025
 
                Common Stock Beneficially Owned:   0 Shares
 
                16% Subordinated Notes Held         (Original Principal Amount):
  $5,066,560.58
 
                18% Subordinated Notes Held         (Original Principal Amount):
  $3,525,536.79

[Recapitalization Letter]

 

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                  KEVIN G. DOUGLAS AND MICHELLE M. DOUGLAS, JTWROS
 
           

  By:                

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               Name: Kevin Douglas              in his capacity as joint tenant
with right of survivorship

  By:                

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               Name: Michelle Douglas              in her capacity as joint
tenant with right of survivorship
 
                Address: 1101 5th Ave., Suite 360                     San
Rafael, CA 94901
 
                Common Stock Beneficially Owned:   0 Shares
 
                16% Subordinated Notes Held         (Original Principal Amount):
  $2,598,236.20
 
                18% Subordinated Notes Held         (Original Principal Amount):
  $                   0

[Recapitalization Letter]

 

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                  DOUGLAS FAMILY TRUST
 
           

  By:                

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               Name: James E. Douglas Jr.              Title: Trustee
 
           

  By:                

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               Name: Jean A. Douglas              Title: Trustee
 
                Address: 1101 5th Ave., Suite 360                     San
Rafael, CA 94901
 
                Common Stock Beneficially Owned:   0 Shares
 
                16% Subordinated Notes Held         (Original Principal Amount):
  $1,299,118.10
 
                18% Subordinated Notes Held         (Original Principal Amount):
  $                   0

[Recapitalization Letter]

 

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                  JAMES DOUGLAS AND JEAN DOUGLAS IRREVOCABLE DESCENDANT’S TRUST
 
           

  By:                

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               Name: Kevin Douglas              Title: Trustee
 
           

  By:                

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               Name: Michelle Douglas              Title: Trustee
 
                Address: 1101 5th Ave., Suite 360                     San
Rafael, CA 94901
 
                Common Stock Beneficially Owned:   0 Shares
 
                16% Subordinated Notes Held         (Original Principal Amount):
  $1,299,118.10
 
                18% Subordinated Notes Held         (Original Principal Amount):
  $                   0

[Recapitalization Letter]

 

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                  B. RILEY & CO. PROFIT SHARING, INC.
 
           

  By:                

--------------------------------------------------------------------------------

               Name: Bryant Riley              Title: Trustee
 
                Address: 11150 Santa Monica Blvd., Suite 750            
        Los Angeles, CA 90025
 
                Common Stock Beneficially Owned:   0 Shares
 
                16% Subordinated Notes Held         (Original Principal Amount):
  $129,911.81
 
                18% Subordinated Notes Held         (Original Principal Amount):
  $                0

[Recapitalization Letter]

 

--------------------------------------------------------------------------------

 

                  B. RILEY & CO., INC.
 
           

  By:                

--------------------------------------------------------------------------------

               Name: Bryant Riley              Title: Chairman
 
                Address: 11150 Santa Monica Blvd., Suite 750            
        Los Angeles, CA 90025
 
                Common Stock Beneficially Owned:   0 Shares
 
                16% Subordinated Notes Held         (Original Principal Amount):
  $844,426.77
 
                18% Subordinated Notes Held         (Original Principal Amount):
  $310,694.38

[Recapitalization Letter]

 

--------------------------------------------------------------------------------

 

                  L. MILLER III GST dtd 12/31/91
 
           

  By:                

--------------------------------------------------------------------------------

               Name: Lloyd I. Miller              Title: Trustee
 
                Address: 4550 Gordon Drive                     Naples, FL 34102
 
                Common Stock Beneficially Owned:   0 Shares
 
                16% Subordinated Notes Held         (Original Principal Amount):
  $324,779.53
 
                18% Subordinated Notes Held         (Original Principal Amount):
  $                0

[Recapitalization Letter]

 

--------------------------------------------------------------------------------

 

                  MILFAM, LLC
 
           

  By:                

--------------------------------------------------------------------------------

               Name: Lloyd I. Miller              Title: General Partner
 
                Address: 4550 Gordon Drive                     Naples, FL 34102
 
                Common Stock Beneficially Owned:   0 Shares
 
                16% Subordinated Notes Held         (Original Principal Amount):
  $324,779.53
 
                18% Subordinated Notes Held         (Original Principal Amount):
  $                0

[Recapitalization Letter]

 

--------------------------------------------------------------------------------

 

                  CATHERINE C. MILLER IRREV TR DTD 3/26/91
 
           

  By:                

--------------------------------------------------------------------------------

               Name: Lloyd I. Miller              Title: Trustee
 
                Address: 4550 Gordon Drive                     Naples, FL 34102
 
                Common Stock Beneficially Owned:   0 Shares
 
                16% Subordinated Notes Held         (Original Principal Amount):
  $324,779.53
 
                18% Subordinated Notes Held         (Original Principal Amount):
  $                0

[Recapitalization Letter]

 

--------------------------------------------------------------------------------

 

                  ALEXANDRA B. MILLER
 
           

  By:                

--------------------------------------------------------------------------------

               Name: Lloyd I. Miller              Title: Custodian FL/UTMA
 
                Address: 4550 Gordon Drive                     Naples, FL 34102
 
                Common Stock Beneficially Owned:   0 Shares
 
                16% Subordinated Notes Held         (Original Principal Amount):
  $324,779.53
 
                18% Subordinated Notes Held         (Original Principal Amount):
  $                0

[Recapitalization Letter]

 

--------------------------------------------------------------------------------

 

                  LLOYD I. MILLER
 
           

  By:                

--------------------------------------------------------------------------------

               Name: Lloyd I. Miller              in his individual capacity
 
                Address: 4550 Gordon Drive                     Naples, FL 34102
 
                Common Stock Beneficially Owned:   0 Shares
 
                16% Subordinated Notes Held         (Original Principal Amount):
  $3,897,354.28
 
                18% Subordinated Notes Held         (Original Principal Amount):
  $3,992,446.11

[Recapitalization Letter]

 

--------------------------------------------------------------------------------

 

                  LLOYD I. MILLER TRUST A-4
 
                By: PNC Bank
 
           

  By:                

--------------------------------------------------------------------------------

               Name: Alan Goldman              Title: Trustee
 
                Common Stock Beneficially Owned:   0 Shares
 
                16% Subordinated Notes Held         (Original Principal Amount):
  $2,598,236,20
 
                18% Subordinated Notes Held         (Original Principal Amount):
  $                   0

[Recapitalization Letter]

 

--------------------------------------------------------------------------------

 

                  MILFAM I, L.P.
 
           

  By:                

--------------------------------------------------------------------------------

               Name: Lloyd I. Miller              Title:   Limited Partner
 
                Address:   4550 Gordon Drive                     Naples, FL
34102
 
                Common Stock Beneficially Owned:   0 Shares
 
                16% Subordinated Notes Held         (Original Principal Amount):
  $2,598,236.20
 
                18% Subordinated Notes Held         (Original Principal Amount):
  $3,992,446.11

[Recapitalization Letter]

 

--------------------------------------------------------------------------------

 

                  MILFAM II, L.P.
 
           

  By:                

--------------------------------------------------------------------------------

               Name: Lloyd I. Miller              Title:   Limited Partner
 
                Address:  4550 Gordon Drive                     Naples, FL 34102
 
                Common Stock Beneficially Owned:   0 Shares
 
                16% Subordinated Notes Held         (Original Principal Amount):
  $2,598,236.20
 
                18% Subordinated Notes Held         (Original Principal Amount):
  $                   0

[Recapitalization Letter]

 

--------------------------------------------------------------------------------

 

                  HIGHLAND CRUSADER OFFSHORE PARTNERS
 
           

  By:                

--------------------------------------------------------------------------------

 

           Name:    

           Title:    
 
                Address:  13455 Noel Road, Suite 1300            
        Dallas, TX 75240
 
                Common Stock Beneficially Owned:   0 Shares
 
                16% Subordinated Notes Held         (Original Principal Amount):
  $5,196,472.40
 
                18% Subordinated Notes Held         (Original Principal Amount):
  $   898,962.84

[Recapitalization Letter]

 

--------------------------------------------------------------------------------

 

                  RICHARD RILEY
 
               

--------------------------------------------------------------------------------

      Name:   Richard Riley         in his individual capacity
 
                Address:   133 Shorecliff Road,                  Corona del Mar,
CA 92625
 
                Common Stock Beneficially Owned:   0 Shares
 
                16% Subordinated Notes Held         (Original Principal Amount):
  $324,779.53
 
                18% Subordinated Notes Held         (Original Principal Amount):
  $                0

[Recapitalization Letter]

 

--------------------------------------------------------------------------------

 

                  BRYANT AND CARLEEN RILEY
 
           

  By:                

--------------------------------------------------------------------------------

               Name: Bryant Riley in his capacity as joint              tenant
with right of survivorship
 
           

  By:                

--------------------------------------------------------------------------------

               Name: Carleen Riley in her capacity as              joint tenant
with right of survivorship
 
                Address:  12710 Marlboro Street                     Brentwood,
CA 90049
 
                Common Stock Beneficially Owned:   0 Shares
 
                16% Subordinated Notes Held         (Original Principal Amount):
  $129,911.81
 
                18% Subordinated Notes Held         (Original Principal Amount):
  $                0

[Recapitalization Letter]

 

--------------------------------------------------------------------------------

 

                  HEDGEHOG CAPITAL
 
           

  By:                

--------------------------------------------------------------------------------

 

           Name:    

           Title:    
 
                Address:  1117 East Putnam Avenue, Suite 320            
        Riverside, CT 06878
 
                Common Stock Beneficially Owned:   0 Shares
 
                16% Subordinated Notes Held         (Original Principal Amount):
  $3,120,000.00
 
                18% Subordinated Notes Held         (Original Principal Amount):
  $                   0

[Recapitalization Letter]

 

--------------------------------------------------------------------------------

 

                  THE CONUS FUND, L.P.
 
           

  By:                

--------------------------------------------------------------------------------

 

           Name:    

           Title:    
 
                Address:  1 Rockefeller Plaza, 18th Floor            
        New York, New York 10020
 
                Common Stock Beneficially Owned:   0 Shares
 
                16% Subordinated Notes Held         (Original Principal Amount):
  $1,096,297.72
 
                18% Subordinated Notes Held         (Original Principal Amount):
  $                   0

[Recapitalization Letter]

 

--------------------------------------------------------------------------------

 

                  EAST HUDSON INC. (BVI)
 
           

  By:                

--------------------------------------------------------------------------------

 

           Name:    

           Title:    
 
                Address:  1 Rockefeller Plaza, 18th Floor            
        New York, New York 10020
 
                Common Stock Beneficially Owned:   0 Shares
 
                16% Subordinated Notes Held         (Original Principal Amount):
  $194,480.00
 
                18% Subordinated Notes Held         (Original Principal Amount):
  $                0

[Recapitalization Letter]

 

--------------------------------------------------------------------------------

 

                  THE CONUS FUND OFFSHORE LIMITED
 
           

  By:                

--------------------------------------------------------------------------------

 

           Name:    

           Title:    
 
                Address:  1 Rockefeller Plaza, 18th Floor            
        New York, New York 10020
 
                Common Stock Beneficially Owned:   0 Shares
 
                16% Subordinated Notes Held         (Original Principal Amount):
  $201,760.00
 
                18% Subordinated Notes Held         (Original Principal Amount):
  $                0

[Recapitalization Letter]

 

--------------------------------------------------------------------------------

 

                  THE CONUS FUND (QP), L.P.
 
           

  By:                

--------------------------------------------------------------------------------

 

           Name:    

           Title:    
 
                Address:  1 Rockefeller Plaza, 18th Floor            
        New York, New York 10020
 
                Common Stock Beneficially Owned:   0 Shares
 
                16% Subordinated Notes Held         (Original Principal Amount):
  $346,320.00
 
                18% Subordinated Notes Held         (Original Principal Amount):
  $                0

[Recapitalization Letter]

 

--------------------------------------------------------------------------------

 

SCHEDULE I

                                                      Shares of Recap     Shares
of New       Term Loan A     Term Loan B     Common Stock to be     Preferred
Stock to   Investor   Commitment     Commitment     Received     be Received  
Elliott Associates, L.P.
  $ —     $ —       5,298,946.0       88,315.8  
Elliott International, L.P.
    —       —       9,636,002.2       160,600.0  
Manchester Securities Corp.
    18,880,491.14       15,023,988.18       9,008,825.9       150,147.1  
Falcon Mezzanine Partners, LP
    —       4,150,000.00       7,280,339.63       121,338.99  
D.E. Shaw Laminar Portfolios, L.L.C.
    —       —       803,567.41       13,392.79  
Langley Partners, L.P.
    338,187.49       450,916.65       612,297.34       10,204.96  
SACC Partners, LP
    —       4,520,000.00       5,193,933.22       86,565.55  
Kevin G. Douglas and Michelle M. Douglas
    —       —       369,314.28       6,155.24  
Douglas Family Trust
    —       —       184,657.14       3,077.62  
James Douglas and Jean Douglas Irrevocable Descendant’s Trust
    —       —       184,657.14       3,077.62  
B. Riley & Co. Profit Sharing, Inc.
    —       80,000.00       70,042.69       1,167.38  
B. Riley & Co., Inc.
    —       350,000.00       459,042.41       7,650.71  
L. Miller III GST dtd 12/31/91
    —       —       29,843.58       497.39  
MilFam LLC
    —       —       29,843.58       497.39  
Catherine C. Miller Irrev Tr dtd 3/26/91
    —       —       29,843.58       497.39  
Alexandra B. Miller
    —       —       29,843.58       497.39  
Lloyd I. Miller
    2,142,857.14       2,857,142.86       4,928,040.82       82,134.01  
Lloyd I. Miller Trust A-4
    1,285,714.29       1,714,285.71       1,998,147.12       33,302.45  
MilFam I, L.P.
    1,285,714.29       1,714,285.71       3,635,734.18       60,595.57  
MilFam II, L.P.
    1,285,714.29       1,714,285.71       1,998,147.12       33,302.45  
Highland Crusader Offshore Partners
    3,428,571.43       4,571,428.57       5,107,470.23       85,124.50  
Richard Riley
    —       —       29,843.58       497.39  
Bryant and Carleen Riley
    —       50,000.00       48,253.22       804.22  
Hedgehog Capital LLC
    351,119.37       1,634,825.82       1,620,809.05       27,013.48  

 

--------------------------------------------------------------------------------

 

                                                      Shares of Recap     Shares
of New       Term Loan A     Term Loan B     Common Stock to be     Preferred
Stock to   Investor   Commitment     Commitment     Received     be Received  
The Conus Fund, L.P.
    597,156.22       696,844.28       842,142.83       14,035.71  
East Hudson Inc. (BVI)
    105,933.76       123,618.13       149,393.67       2,489.89  
The Conus Fund Offshore Ltd.
    109,899.20       128,245.55       154,985.95       2,583.10  
The Conus Fund (QP), L.P.
    188,641.40       220,132.82       266,032.57       4,433.88  
 
                       
 
  $ 30,000,000     $ 40,000,000       60,000,000       1,000,000  

 

--------------------------------------------------------------------------------

 

SCHEDULE II

Each of the Purchase Agreement related to the Company’s 18% Subordinated Secured
Notes due March 31, 2007 and the Purchase Agreement related to the Company’s 16%
Subordinated Secured Notes due March 31, 2007 (in each case before giving effect
to paragraph 1 of the letter agreement to which this Schedule II is attached) is
amended, by execution of the letter agreement, without the need for further act
or evidence, to delete therefrom:

     Terms of the Notes: Section 2.2(c)

     Covenants: All of Article 6

     Events of Default: All of Section 7.1, except Sections 7.1.1, 7.1.4, 7.1.6
and 7.1.8

provided, however, if required by the holders of a majority of the outstanding
Subordinated Notes, in lieu of deletion of certain affirmative covenants, those
covenants may be retained and amended or revised as would be appropriate for
publicly traded debt securities of an investment grade issuer.

[Recapitalization Letter]

 

--------------------------------------------------------------------------------

 

Exhibit A

HORIZON OFFSHORE, INC.

CERTIFICATE OF DESIGNATION,
PREFERENCES AND RIGHTS
OF
SERIES B MANDATORILY CONVERTIBLE REDEEMABLE

PREFERRED STOCK

--------------------------------------------------------------------------------

Pursuant to Section 151 of the
Delaware General Corporation Law

--------------------------------------------------------------------------------

      HORIZON OFFSHORE, INC. (the “Company”), a corporation organized and
existing under the laws of the State of Delaware, hereby certifies that pursuant
to the provisions of Section 151 of the Delaware General Corporation Law, its
Board of Directors, at a duly noticed and convened meeting held on March 29,
2005 adopted the following resolution, which resolution remains in full force
and effect as of the date hereof:

      WHEREAS, the Board of Directors of the Company is authorized, within the
limitations and restrictions stated in the Certificate of Incorporation, to fix
by resolution or resolutions the designation of preferred stock and the powers,
preferences and relative participating, optional or other special rights and
qualifications, limitations or restrictions thereof, including, without limiting
the generality of the foregoing, such provisions as may be desired concerning
voting, redemption, dividends, dissolution or the distribution of assets,
conversion or exchange, and such other subjects or matters as may be fixed by
resolution or resolutions of the Board of Directors under the Delaware General
Corporation Law; and

      WHEREAS, it is the desire of the Board of Directors of the Company,
pursuant to its authority as aforesaid, to authorize and fix the terms of the
preferred stock to be designated the Series B Mandatorily Convertible Redeemable
Preferred Stock of the Company and the number of shares constituting such
preferred stock;

      NOW, THEREFORE, BE IT RESOLVED, that there is hereby authorized the
Series B Mandatorily Convertible Redeemable Preferred Stock on the terms and
with the provisions herein set forth:

1

--------------------------------------------------------------------------------

 

DESIGNATION, PREFERENCES AND RIGHTS

of

SERIES B MANDATORILY CONVERTIBLE REDEEMABLE PREFERRED STOCK

of

HORIZON OFFSHORE, INC.

      The relative rights, preferences, powers, qualifications, limitations and
restrictions granted to or imposed upon the Series B Mandatorily Convertible
Redeemable Preferred Stock or the holders thereof are as follows:

      1. Definitions. For purposes of this Certificate of Designation,
Preferences and Rights of Series B Mandatorily Convertible Redeemable Preferred
Stock (this “Certificate of Designation”) the following definitions shall apply:

      “Amendment” shall mean receipt by the Company from the Delaware Secretary
of State of confirmation of filing of a Certificate of Amendment of the
Company’s Certificate of Incorporation, as amended, that (a) increases the
number of authorized shares of Common Stock to one billion shares and
(b) reduces the par value for such shares to not more than $.00001 per share
duly approved and adopted by the Board and the Company’s stockholders in
accordance with Section 242 of the Delaware General Corporation Law and all
other applicable laws, rules and regulations.

      “Board” shall mean the Board of Directors of the Company.

      “Common Stock” shall mean the Common Stock, par value $1.00 per share, of
the Company, as constituted from time to time; provided however, the Common
Stock as constituted from time to time shall have only the voting powers and
rights appurtenant to the Common Stock existing at the Original Issue Date.

      “Company” shall mean Horizon Offshore, Inc., a Delaware corporation.

      “Conversion Rate” has the meaning set forth in Section 7(a) of this
Certificate of Designation.

      “Current Market Price,” when used with reference to shares of Common Stock
or other securities on any date, shall mean the average of the daily market
prices for 20 consecutive trading days commencing 30 days before such date. The
daily market price for each such trading day shall be the average of the last
reported closing bid and asked prices on such day as officially quoted on the
NASDAQ National Market, (a) if the Common Stock is not then listed or admitted
to trading on any stock exchange or such market, the average of the last
reported closing bid and asked prices on such day on the OTC Bulletin Board (or
similar system on such day) as furnished by NASDAQ or Pink Sheets, LLC, (b) if
neither such entity at the time is engaged in the business of reporting

2

--------------------------------------------------------------------------------

 

such prices, as furnished by any similar firm then engaged in such business, or
(c) if there is no such firm, as furnished by any member of the National
Association of Securities Dealers (“NASD”) selected mutually by the Required
Holders and the Company or, if they cannot agree upon such selection, as
selected by two such members of the NASD, one of which shall be selected by the
Required Holders and one of which shall be selected by the Company.

      “Fully Diluted Outstanding” shall mean, with reference to Common Stock, at
any date as of which the number of shares thereof is to be determined, (a) all
shares of Common Stock outstanding at such date and (b) all shares of Common
Stock underlying other options or warrants to purchase, or other securities
convertible into or exchangeable for, shares of Common Stock outstanding on such
date excluding any such options, warrants or securities with an exercise or
conversion price in excess of the Current Market Price.

      “Liquidation Preference” shall mean $40.00 per share for each share of the
Mandatorily Convertible Preferred Stock.

      “Mandatorily Convertible Preferred Stock” shall refer to shares of
Series B Mandatorily Convertible Redeemable Participating Preferred Stock, $1.00
par value per share, of the Company.

      “Original Issue Date” shall mean the date of the original issuance of
shares of Mandatorily Convertible Preferred Stock.

      “Person” shall mean any individual, firm, corporation or other entity, and
shall include any successor (by merger or otherwise) of such entity.

      “Redemption Date” shall mean March 31, 2011.

      “Redemption Price” shall mean, at any date of determination, a per share
amount equal to the Liquidation Preference hereof increased at a rate of 10% per
annum, compounded quarterly at the end of each fiscal quarter of the Company
(commencing June 30, 2005).

      “Required Holders” shall mean the holders of at least of a majority of the
outstanding shares of Mandatorily Convertible Preferred Stock.

      “Six Month Anniversary Date” has the meaning set forth in Section 7(a) of
this Certificate of Designation.

      2. Designation; Number of Shares. The designation of the preferred stock
authorized by this resolution shall be “Series B Mandatorily Convertible
Redeemable Participating Preferred Stock” and the number of shares of Series B
Mandatorily Convertible Redeemable Participating Preferred Stock authorized
hereby shall be 1,000,000 shares.

3

--------------------------------------------------------------------------------

 

      3. Dividends.

      (a) No dividends shall be declared or paid on shares of Mandatorily
Convertible Preferred Stock.

      (b) So long as any shares of Mandatorily Convertible Preferred Stock shall
be outstanding, no dividend whatsoever shall be paid or declared, and no
distribution shall be made, on account of any Common Stock or of Common Stock
(or any security convertible or exchangeable therefor.

      4. Liquidation Rights of Mandatorily Convertible Preferred Stock.

      (a) In the event of any liquidation, dissolution or winding up of the
Company, whether voluntary or involuntary, the holders of Mandatorily
Convertible Preferred Stock then outstanding shall be entitled to be paid out of
the assets of the Company available for distribution to its stockholders,
whether such assets are capital, surplus or earnings, before any payment or
declaration and setting apart for payment of any amount shall be made in respect
of any shares of Common Stock or any share of any other class or series of the
Company’s preferred stock ranking junior to the Mandatorily Convertible
Preferred Stock with respect to the payment of dividends or distribution of
assets on liquidation, dissolution or winding up of the Company, an amount in
cash equal to the greater of (i) the Liquidation Preference and (ii) such amount
per share as would have been payable had each such share been converted to
Common Stock pursuant to Section 7 immediately prior to such liquidation,
dissolution or winding up of the Company.

      (b) If upon any liquidation, dissolution or winding up of the Company,
whether voluntary or involuntary, the assets to be distributed among the holders
of Mandatorily Convertible Preferred Stock shall be insufficient to permit the
payment to such stockholders of the full preferential amounts aforesaid, then
the entire assets of the Company to be distributed shall be distributed ratably
among the holders of Mandatorily Convertible Preferred Stock, based on the full
preferential amounts for the number of shares of Mandatorily Convertible
Preferred Stock held by each holder.

      (c) After payment to the holders of Mandatorily Convertible Preferred
Stock of the amounts set forth in Section 4(a) hereof, the entire remaining
assets and funds of the Company legally available for distribution, if any,
shall be distributed among the holders of any Company stock entitled to a
preference over the Common Stock in accordance with the terms thereof and,
thereafter, to the holders of Common Stock.

4

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      5. Voting Rights. Holders of Mandatorily Convertible Preferred Stock shall
have no voting rights, except as provided by law; provided, however that the
affirmative vote of the Required Holders, voting together as a class, in person
or by proxy, at a special or annual meeting of such holders called for the
purpose, or pursuant to a written consent of such holders, shall be necessary
to:

      (a) authorize, adopt or approve an amendment or alteration to, or repeal
of, the Certificate of Incorporation of the Company (whether pursuant to
Section 242 or 251(e) of the Delaware General Corporation Law, merger,
consolidation or otherwise) which would alter or change in any manner the terms,
powers, preferences or special rights of the shares of the Mandatorily
Convertible Preferred Stock or grant waivers thereof, or which would otherwise
adversely affect the rights of the Mandatorily Convertible Preferred Stock,
provided that no such modification or amendment may, without the consent of each
holder of Mandatorily Convertible Preferred Stock affected thereby; (i) change
the Conversion Rate; (ii) change the Redemption Date; (iii) reduce the
Liquidation Preference or Redemption Price of the Mandatorily Convertible
Preferred Stock; or (iv) reduce the percentage of outstanding Mandatorily
Convertible Preferred Stock necessary to modify or amend the terms thereof or to
grant waivers thereof; or

      (b) issue any shares of the Common Stock, or shares of other capital stock
of the Company ranking senior to, or pari passu with, or junior to (either as to
dividends or upon voluntary or involuntary liquidation, dissolution or winding
up) the Mandatorily Convertible Preferred Stock, or issue any securities, notes,
warrants, options or other instruments convertible into, exercisable for or
exchangeable for such shares.

      6. Redemption of Mandatorily Convertible Preferred Stock.

      (a) The Company shall redeem, and the holders of the outstanding
Mandatorily Convertible Preferred Stock shall sell to the Company on the
Redemption Date, for cash at the Redemption Price, all of the outstanding
Mandatorily Convertible Preferred Stock.

      (b) On or before the Redemption Date, each holder of Mandatorily
Convertible Preferred Stock shall surrender the certificate or certificates
representing such shares of Mandatorily Convertible Preferred Stock to the
Company, in the manner and at the place designated in the written notice of
redemption provided by the Company, and thereupon the Redemption Price for such
shares shall be payable in the manner described in Section 6(c) on the
Redemption Date to the person whose name appears on such certificate or
certificates as the owner thereof, and each surrendered certificate shall be
cancelled and retired.

      (c) The Redemption Price shall be payable in cash at the Redemption Date
upon any redemption pursuant to Section 6(a).

      (d) Unless the Company shall fail to redeem the shares of Mandatorily
Convertible Preferred Stock when the Company is required to do so, the holders
of shares

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of Mandatorily Convertible Preferred Stock which are to be redeemed shall cease
to have any further rights with respect thereto on the Redemption Date, other
than to receive the applicable Redemption Price, which shall be without
interest.

      (e) If, at the time of any redemption pursuant to Section 6(a), the funds
of the Company legally available for redemption of Mandatorily Convertible
Preferred Stock are insufficient to redeem the number of shares required to be
redeemed, those funds which are legally available shall be used to redeem the
maximum possible number of such shares, pro rata based upon the number of shares
to be redeemed. At any time thereafter when additional funds of the Company
become legally available for the redemption of Mandatorily Convertible Preferred
Stock, such funds shall immediately be used to redeem the balance of the shares
of Mandatorily Convertible Preferred Stock which the Company has become
obligated to redeem pursuant to this Section 6(e).

      (f) The Company may not otherwise redeem or repurchase the Mandatorily
Convertible Preferred Stock.

      7. Conversion.

      (a) Automatic Conversion. Upon the occurrence of the Amendment, all the
shares of Mandatorily Convertible Preferred Stock shall automatically convert
into fully paid and nonassessable shares of Common Stock at the Conversion Rate;
provided, however, if the Amendment occurs prior to the date which is six months
and one day from and after the Original Issue Date ( the “Six Month Anniversary
Date”), no conversion will occur until the Six Month Anniversary Date . The
“Conversion Rate” means, for each share of Mandatorily Convertible Preferred
Stock, a number of shares of Common Stock calculated as follows:

Conversion Rate = (X — [60,000,000 plus the number of Fully Diluted Outstanding
Shares of Common Stock on March 31, 2005])/1,000,000;

where X equals the number of Fully Diluted Outstanding shares of Common Stock on
March 31, 2005 divided by .05, as such rate may be adjusted from time to time as
provided in Section 7(e) below.

      (b) Fractional Shares. No fractional shares of Common Stock will be issued
upon conversion of the Mandatorily Convertible Preferred Stock. In lieu of
fractional shares, the Company will round up to the nearest whole share the
number of shares of Common Stock issued upon conversion of the Mandatorily
Convertible Preferred Stock.

      (c) Exchange of Certificates. The conversion of the Mandatorily
Convertible Preferred Stock into Common Stock shall be effective immediately
upon public announcement by the Company of the automatic conversion provided for
in Section 7(a) and each certificate representing shares of Convertible
Preferred Stock shall then be deemed thereafter to represent shares of Common
Stock without any further

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action on the part of the holders of such shares and whether or not the
certificates representing such shares are surrendered to the Company; provided,
however, that promptly after such conversion, the Company shall provide notice
of such conversion to the holders of the Convertible Preferred Stock and from
and after such notice, each holder will be entitled to surrender the certificate
or certificates for the shares of Mandatorily Convertible Preferred Stock at the
office of the transfer agent (or at the principal office of the Company if the
Company serves as its own transfer agent) together with a notice as to whether
the certificate or certificates for shares of Common Stock to be issued shall be
in such holder’s name or the names of such holder’s nominee(s). If required by
the Company, certificates surrendered after conversion will be endorsed or
accompanied by a written instrument or instruments of transfer, in form
reasonably satisfactory to the Company, duly executed by the holder or his, her
or its attorney duly authorized in writing. The Company will, as soon as
practicable after the Amendment, issue and deliver at such office to such
holder, or to such holder’s nominee(s), a certificate or certificates for the
number of shares of Common Stock to which such holder is entitled. Such
conversion will be deemed to have been made immediately after the Amendment, and
the Person or Persons entitled to receive the shares of Common Stock issuable
upon such conversion will be treated for all purposes as the record holder or
holders of such shares of Common Stock as of such date.

      (d) Stock Splits, Dividends and Distributions. So long as any shares of
Mandatorily Convertible Preferred Stock are outstanding, the Company will not
effect any split or subdivision of the outstanding shares of Common Stock.

      (e) Adjustment for Reorganization, Reclassification or Exchange. If the
Common Stock issuable upon the conversion of the Mandatorily Convertible
Preferred Stock is changed into or exchanged for the same or a different number
of shares of any class or classes of stock of the Company or another entity,
whether by capital reorganization, merger, consolidation, reclassification, or
otherwise then and in each such event the holders will have the right upon
conversion to receive such shares of the kind and amount of shares of stock and
other securities and property receivable upon such capital reorganization,
merger, consolidation, reclassification, or other change such that its
conversion rights and the Conversion Rate with respect to Common Stock of the
Company or such other entity will be maintained upon the occurrence of the
Amendment.

      (f) No Impairment. The Company will not, by amendment of its Certificate
of Incorporation or through any reorganization, transfer of assets,
consolidation, merger, dissolution, issue or sale of securities or any other
voluntary action, modify, amend, abrogate, avoid or seek to avoid the observance
or performance of any of the terms to be observed or performed hereunder by the
Company, but will at all times in good faith assist in the carrying out of all
the provisions of this Certificate of Designation and in the taking of all such
action as may be necessary or appropriate to protect the conversion rights and
other rights and preferences of the holders of the Mandatorily Convertible
Preferred Stock against impairment.

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      (g) Certificate as to Adjustments. The Company will, upon the written
request at any time of any holder of Mandatorily Convertible Preferred Stock,
furnish or cause to be furnished to such holder a certificate setting forth the
number of shares of Common Stock and the amount, if any, of other property which
then would be received upon the conversion of Mandatorily Convertible Preferred
Stock.

      8. Remedies. Any registered holder of Mandatorily Convertible Preferred
Stock may proceed to protect and enforce its rights and the rights of such
holders by any available remedy by proceeding at law or in equity to protect and
enforce any such rights, whether for the specific enforcement of any provision
in this Certificate of Designation or in aid of the exercise of any power
granted herein, or to enforce any other proper remedy.

      9. No Reissuance of Mandatorily Convertible Preferred Stock. No
Mandatorily Convertible Preferred Stock acquired by the Company by reason of
redemption, purchase, or otherwise shall be reissued, and all such shares shall
be cancelled, retired and eliminated from the shares which the Company shall be
authorized to issue.

      10. Notices. All notices to the Company permitted hereunder shall be
personally delivered or sent by first class mail, postage prepaid, addressed to
its principal office located at 2500 CityWest Boulevard, Suite 2200, Houston,
Texas 77042, or to such other address at which its principal office is located
and as to which notice thereof is similarly given to the holders of the
Mandatorily Convertible Preferred Stock at their addresses appearing on the
books of the Company.

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      11. Legend. Each certificate representing shares of Mandatorily
Convertible Preferred Stock shall bear the following legend:

“THE SECURITIES EVIDENCED BY THIS CERTIFICATE HAVE BEEN ACQUIRED FOR INVESTMENT
AND THE OFFER AND SALE OF THESE SECURITIES HAVE NOT BEEN REGISTERED UNDER THE
SECURITIES ACT OF 1933 OR ANY STATE SECURITIES OR BLUE SKY LAWS. THESE
SECURITIES MAY NOT BE SOLD OR TRANSFERRED IN THE ABSENCE OF SUCH REGISTRATION OR
AN EXEMPTION THEREFROM UNDER SAID ACT OR APPLICABLE STATE SECURITIES OR BLUE SKY
LAWS. ADDITIONALLY, THE TRANSFER OF THESE SECURITIES IS SUBJECT TO THE
CONDITIONS SPECIFIED IN A LETTER AGREEMENT DATED AS OF MARCH 31, 2005, AMONG THE
ISSUER HEREOF AND CERTAIN OTHER PARTIES THERETO, AND NO TRANSFER OF THESE
SECURITIES SHALL BE VALID OR EFFECTIVE UNTIL SUCH CONDITIONS HAVE BEEN
FULFILLED. A COPY OF SUCH AGREEMENT MAY BE OBTAINED AT NO COST BY WRITTEN
REQUEST MADE BY THE HOLDER OF RECORD OF THIS CERTIFICATE TO THE SECRETARY OF THE
ISSUER HEREOF.”

[Remainder of Page Intentionally Left Blank]

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      IN WITNESS WHEREOF, Horizon Offshore, Inc. has caused this Certificate to
be signed by its President and Secretary, respectively, on this 31 day of March,
2005.

         

       

  President    

       

       

       

  Secretary