<PAGE>   1
                                                                    EXHIBIT 3(i)




           SECOND AMENDED AND RESTATED CERTIFICATE OF INCORPORATION OF
                          AMERICAN CLASSIC VOYAGES CO.

         American Classic Voyages Co. (the "Corporation"), a corporation
organized and existing under the laws of the State of Delaware, hereby certifies
as follows:

         1. The name of the Corporation is American Classic Voyages Co. American
Classic Voyages Co. was originally incorporated under the name DQSC, Inc., and
the original Certificate of Incorporation of the Corporation was filed with the
Secretary of State of the State of Delaware on June 19, 1985.

         2. The Board of Directors of the Corporation, by unanimous written
consent of its members, filed with the minutes of the board, adopted resolutions
proposing and declaring advisable that the Certificate of Incorporation be
amended and restated.

         3. In lieu of a meeting and vote of stockholders, the holders of a
majority of the outstanding shares of common stock have given their written
consent to said amended and restated Certificate of Incorporation in accordance
with the provisions of Section 228 of the Delaware General Corporation Law.

         4. Pursuant to Sections 242 and 228 of the General Corporation Law of
the State of Delaware, this Second Amended and Restated Certificate of
Incorporation ("Second Amended and Restated Certificate") restates and
integrates and further amends the provisions of the Certificate of Incorporation
of this Corporation.

         5. The text of the Certificate of Incorporation as heretofore amended
or supplemented is hereby restated and further amended to read in its entirety
as follows:

                  FIRST: The name of the Corporation is American Classic Voyages
Co.

                  SECOND: The registered office of the Corporation is to be
located at 1013 Centre Road, Wilmington, in the County of Kent, the State of
Delaware, 19805-1297. The name of its registered agent at that address is The
Prentice-Hall Corporation System, Inc.

                  THIRD: The purpose of the Corporation is to engage in any
lawful act or activity for which a corporation may be organized under the
General Corporation Law of Delaware.

                  FOURTH: The maximum number of shares of capital stock which
the Corporation is authorized to issue or to have outstanding at any time shall
be 45,000,000 shares of which 40,000,000 shall be Common Stock of $.01 (one
cent) par value, and 5,000,000 shall be Preferred Stock of $.01 (one cent) par
value. The Preferred Stock may be issued from time to time in one or more
series, upon resolution or resolutions providing for such series adopted by the
Board of Directors, with such distinctive designations as shall be stated in
such resolution or resolutions. The resolution or resolutions providing for the
issue of shares of a particular series shall fix, subject to the applicable laws
and provisions of this Article FOURTH, the designation, rights, preferences and
limitations of the shares of each such series. The authority of the Board of
Directors with respect to each series shall include, but not be limited to, the
determination of the following:


<PAGE>   2

                  (a)      The number of shares constituting such series,
                           including the authority to increase or decrease such
                           number, and the distinctive designation of such
                           series;

                  (b)      The dividend rate of the shares of such series,
                           whether the dividends shall be cumulative and, if so,
                           the date from which they shall be cumulative, and the
                           relative rights of priority, if any, of payment of
                           dividends on shares of such series;

                  (c)      The right, if any, of the Corporation to redeem
                           shares of such series and the terms and conditions of
                           such redemption including the redemption price;

                  (d)      The rights of the shares in case of a voluntary or
                           involuntary liquidation, dissolution or winding up of
                           the Corporation, and the relative rights of priority,
                           if any, of payment of shares of such series;

                  (e)      The voting rights, if any, for such series and the
                           terms and conditions under which such voting rights
                           may be exercised;

                  (f)      The obligation, if any, of the Corporation to retire
                           shares of such series pursuant to a retirement or
                           sinking fund or fund of a similar nature and the
                           terms and conditions of such obligation;

                  (g)      The terms and conditions, if any, upon which shares
                           of such series shall be convertible into or
                           exchangeable for shares of stock of any other class
                           or classes or of any other series of preferred stock,
                           including the price or prices or the rate or rates of
                           conversion or exchange and the terms of adjustment,
                           if any; and

                  (h)      Any other rights, preferences or limitations of the
                           shares of such series as may be permitted by law.

                  FIFTH: The following provisions are inserted for the
management of the business and for the conduct of the affairs of the
Corporation, and for further definition, limitation and regulation of the powers
of the Corporation and of its directors and stockholders:

                  (a)      The number of directors of the Corporation shall be
                           such as from time to time shall be fixed by, or in
                           the manner provided in, the by-laws. Election of
                           directors need not be by ballot unless the by-laws so
                           provide.

                  (b)      The Board of Directors shall have power without the
                           assent or vote of the stockholders to make, alter,
                           amend, change, add to or repeal the by-laws of the
                           Corporation; to fix and vary the amount to be
                           reserved for any proper purpose; to authorize and
                           cause to be executed mortgages and liens upon all or
                           any part of the property of the Corporation; to
                           determine the use and disposition of any surplus or
                           net profits; and to fix the times for the declaration
                           and payment of dividends.


                                       2
<PAGE>   3

                  (c)      The Board of Directors in their discretion may submit
                           any contract or act for approval or ratification at
                           any annual meeting of the stockholders or at any
                           meeting of the stockholders called for the purpose of
                           considering any such act or contract, and any
                           contract or act that shall be approved or be ratified
                           by the vote of the holders of a majority of the stock
                           of the Corporation which is represented in person or
                           by proxy at such meeting and entitled to vote thereat
                           (provided that a lawful quorum of stockholders be
                           there represented in person or by proxy) shall be as
                           valid and as binding upon the Corporation and upon
                           all the stockholders as though it had been approved
                           or ratified by every stockholder of the Corporation,
                           whether or not the contract or act would otherwise be
                           open to legal attack because of the interest of any
                           member of the Board of Directors, or for any other
                           reason.

                  (d)      In addition to the powers and authorities
                           hereinbefore or by statute expressly conferred upon
                           them, the Board of Directors is hereby empowered to
                           exercise all such powers and do all such acts and
                           things as may be exercised or done by the
                           Corporation; subject, nevertheless, to the provisions
                           of the statutes of the State of Delaware, of this
                           Second Amended and Restated Certificate, and to any
                           by-laws from time to time made by the stockholders;
                           provided, however, that no by-laws so made shall
                           invalidate any prior act of the Board of Directors
                           which would have been valid if such by-law had not
                           been made.

                  SIXTH:

                  (a)      The Corporation shall, to the full extent permitted
                           by Section 145 of the Delaware General Corporation
                           Law, as amended from time to time, indemnify all
                           persons whom it may indemnify pursuant thereto;
                           including, without limitation, (i) any person who was
                           a party to any threatened, pending or completed
                           action or suit by or in the right of the Corporation
                           to procure a judgment in its favor by reason of the
                           fact that such person is or was a director, officer,
                           employee or agent of the Corporation or is or was
                           serving at the request of the Corporation as a
                           director, officer, employee or agent of another
                           corporation, partnership, joint venture, trust or
                           other enterprise, against expenses (including
                           attorneys' fees) actually and reasonably incurred by
                           such person in connection with the defense or
                           settlement of such action or suit, and (ii) any
                           person who was or is party or is threatened to be
                           made a party to any threatened, pending or completed
                           action, suit or proceeding, whether civil, criminal,
                           administrative or investigative (other than an action
                           by or in the right of the Corporation) by reason of
                           the fact that he is or was a director, officer,
                           employee or agent of the Corporation, partnership,
                           joint venture, trust or other enterprise, against
                           expenses (including attorneys' fees), judgments,
                           fines and amounts paid in connection with any such
                           action, suit or proceeding, in each case to the
                           fullest extent permissible under Section 145 of the
                           Delaware General Corporation Law, as amended from
                           time to time, or the indemnification provisions of
                           any successor statute.


                                       3
<PAGE>   4

                  (b)      The foregoing provisions of this Article SIXTH shall
                           be deemed to be a contract between the Corporation
                           and each director, officer, employee or agent of the
                           Corporation or person who is or was serving at the
                           request of the Corporation as a director, officer,
                           employee or agent of another corporation,
                           partnership, joint venture, trust or other enterprise
                           and who serves in such capacity at any time while
                           this Article SIXTH is in effect, and any repeal or
                           modification thereof shall not affect any rights or
                           obligations then existing with respect to any state
                           of facts then or therefore existing or any action,
                           suit or proceedings theretofore or thereafter brought
                           based in whole or in part upon any such state of
                           facts. The foregoing rights of indemnification shall
                           not be deemed exclusive of any other rights to which
                           any director or officer may be entitled apart from
                           the provisions of this Article SIXTH. The Board of
                           Directors in its discretion shall have power on
                           behalf of the Corporation to enter into agreements
                           with respect to the indemnification of any person,
                           other than a director or officer, made a party to any
                           action, suit or proceeding by reason of the fact that
                           he/she, his/her testator or intestate, is or was an
                           employee, agent or otherwise acting on behalf of the
                           Corporation or serving at the request of the
                           Corporation as a director, officer, employee or agent
                           of another corporation, partnership, joint venture,
                           trust or other enterprise.

                  SEVENTH: A director of the Corporation shall not be personally
liable to the Corporation or its stockholders for monetary damages for beach of
fiduciary duty as a director, except for liability (i) for any breach of the
director's duty of loyalty to the Corporation or its stockholders, (ii) for acts
or omissions not in good faith or which involve intentional misconduct or a
knowing violation of law, (iii) under Section 174 of the Delaware General
Corporation Law, or (iv) for any transaction from which the director derived any
improper personal benefit. If the Delaware General Corporation Law is amended
after this Second Amended and Restated Certificate of Incorporation becomes
effective to authorize corporate action further eliminating or limiting the
personal liability of directors, then the liability of a director of the
Corporation shall be eliminated or limited to the fullest extent permitted by
the Delaware General Corporation Law, as so amended.

         Any repeal or modification of the provisions of this Article SEVENTH by
the stockholders of the Corporation shall be prospective only and shall not
adversely affect any limitation on the personal liability of a director of the
Corporation with respect to any act or omission occurring prior to the effective
date of such appeal or modification. In the event that any of the provisions of
this Article SEVENTH (including any provision within a single sentence) is held
by a court of competent jurisdiction to be invalid, void or otherwise
unenforceable, the remaining provisions are severable and shall remain
enforceable to the fullest extent permitted by law.

                  EIGHTH: The Corporation reserves the right to amend, alter,
change or repeal any provision contained in this Second Amended and Restated
Certificate in the manner now or hereafter prescribed by law, and all rights and
powers conferred herein on stockholders, directors and officers are subject to
this reserved power.

                  NINTH: This Second Amended and Restated Certificate is
effective as of 7:30 A.M., Eastern Standard Time, on March 31, 1999.


                                       4
<PAGE>   5

                  TENTH:

                       (A) For purposes of this Article TENTH:

                           (1) The term "Act" shall mean the Securities Exchange
         Act of 1934, as amended.

                           (2) The terms "Affiliate" and "Associate" shall have
         meanings ascribed to them in Rule 12b-2 of the General Rules and
         Regulations under the Act.

                           (3) The terms "acquire", "acquisition" or "acquiring"
         with respect to the acquisition of any security of the corporation
         shall refer to the acquisition of such security by any means
         whatsoever, including, without limitation, an acquisition of such
         security by operation of law, by will or by intestacy.

                           (4) The term "Common Stock" means all common stock of
         the Corporation and any other securities issued by the Corporation
         which are treated as stock for purposes of Section 2 of the Shipping
         Act, 1916.

                           (5) The term "Excess Shares" shall have the meaning 
         ascribed to it in Section (C)(1) hereof.

                           (6) The term "Holder of Excess Shares" shall have the
         meaning ascribed to it in Section (B) hereof.

                           (7) The term "25% Limitation" shall mean the
         limitations on ownership of Common Stock imposed by this Article TENTH.

                           (8) The terms "own", "owned", "ownership" or "owning"
         refer to the ownership of stock in a corporation within the meaning of
         Section 2 of the Shipping Act, 1916.

                           (9) The term "Permitted Transferee" shall have the 
         meaning ascribed to it in Section (C)(1)(a) hereof.

                           (10) The term "Person" shall mean any individual,
         firm, corporation, partnership, joint venture or other entity and shall
         include any group comprised of such Person and any other Person with
         whom such Person or any Affiliate or Associate of such Person has any
         agreement, arrangement or understanding, directly or indirectly, for
         the purpose of acquiring, holding, voting or disposing of Common Stock
         and any other Person who is a member of such group, but does not
         include any underwriter which participates in an underwritten public
         offering of the Corporation's Common Stock, provided that such
         underwriter shall not own such Common Stock.

                           (11) The term "Proceeds" shall have the meaning
         ascribed to it in Section (C)(1)(d) hereof.

                           (12) The term "Purported Owner" shall have the
         meaning ascribed to it in Section (C)(1) hereof.



                                       5
<PAGE>   6

                           (13) The term "Purported Owner's Transferor" shall
         have the meaning ascribed to it in Section (C)(1)(a) hereof.

                           (14) The term "Share Trustee" shall mean the trustee
         of the Excess Shares nominated and appointed by the Board of Directors
         from time to time.

                           (15) The term "Shipping Act" shall mean the Shipping
         Act, 1916, and all amendments thereto as codified in 46 U.S.C. Section
         801, et. seq. and all regulations promulgated thereunder.

                           (16) The term "Transfer Agent" shall mean the
         transfer agent with respect to the Common Stock nominated and appointed
         by the Board of Directors from time to time.

                  (B)      At no time shall any Person who is not a citizen of 
the United States own or purchase Common Stock which, when aggregated with all
other Common Stock of the Corporation owned by Persons who are not citizens of
the United States, would make the ownership of the Common Stock owned by Persons
who are not citizens of the United States exceed twenty-five percent (25%) (the
"25% Limitation") of the total Common Stock.

                  (C)      (1) The transfer, purchase or ownership of any shares
of Common Stock in violation of Section B of this Article TENTH is prohibited
and shall be null and void. If, notwithstanding the foregoing prohibition, a
Person shall, voluntarily or involuntarily, become or attempt to become the
purported owner (the "Purported Owner") of shares of Common Stock, or both, in
excess of such 25% Limitation (the number of shares of Common Stock so exceeding
the 25% Limitation being herein the "Excess Shares"), then:

                           (a)      The Purported Owner shall not obtain any
                                    rights in and to the Excess Shares, and the
                                    purported transfer of the Excess Shares to
                                    the Purported Owner shall not be recognized
                                    by the Transfer Agent. Until the Excess
                                    Shares are transferred to a person whose
                                    acquisition thereof will not violate the 25%
                                    Limitation (a "Permitted Transferee"), the
                                    transferor of the Excess Shares to the
                                    Purported Owner (the "Purported Owner's
                                    Transferor") shall be deemed to have
                                    retained the Excess Shares and shall hold
                                    and be entitled to exercise all rights
                                    incident to ownership of such Excess Shares.
                                    All Excess Shares will continue to be issued
                                    and outstanding.

                           (b)      If the Transfer Agent obtains possession of
                                    a certificate or certificates representing
                                    the Excess Shares, the Transfer Agent shall
                                    deliver such certificate or certificates to
                                    the Share Trustee who shall proceed
                                    forthwith to sell or cause the sale of the
                                    Excess Shares to a Permitted Transferee.
                                    Upon notice from the Corporation of the
                                    existence of Excess Shares and the identity
                                    of the Purported Owner, the Share Trustee
                                    shall take all lawful action to cause the
                                    Purported Owner to deliver or cause delivery
                                    of the Excess Shares and any indicia of
                                    ownership thereof to the Share Trustee and
                                    upon obtaining possession thereof, the Share
                                    Trustee shall proceed forthwith to sell or
                                    cause the sale of the Excess Shares to a
                                    Permitted Transferee. The Share Trustee
                                    shall sell or cause the sale of the 


                                       6
<PAGE>   7

                                    Excess Shares in the then existing public
                                    market or in such other commercially
                                    reasonable fashion as the Corporation shall
                                    direct. In performing the duties herein
                                    imposed upon it, the Share Trustee shall act
                                    at all times as the agent for the Purported
                                    Owner's Transferor.

                           (c)      Once the Excess Shares are acquired by a
                                    Permitted Transferee, the Permitted
                                    Transferee shall have and shall be entitled
                                    to exercise all rights incident to the
                                    ownership of such Excess Shares.

                           (d)      The proceeds from the sale of the Excess
                                    Shares to the Permitted Transferee (the
                                    "Proceeds") shall be distributed as follows:
                                    (i) first, to the Share Trustee for any
                                    costs incurred in respect of its
                                    administration of the Excess Shares, (ii)
                                    second, to the Purported Owner, if known, in
                                    an amount up to the amount paid by the
                                    Purported Owner, if determinable, for the
                                    Excess Shares, and (iii) the remaining
                                    Proceeds, if any, shall be distributed to
                                    the Purported Owner's Transferor, if known,
                                    and if not known, such remaining Proceeds
                                    shall be held by the Corporation for the
                                    benefit of the Purported Owner's Transferor
                                    or such other Person as their interests may
                                    appear. Notwithstanding anything in this
                                    Article TENTH to the contrary, the
                                    Corporation shall at all times be entitled
                                    to make application to any court of
                                    equitable jurisdiction within the State of
                                    Delaware for an adjudication of the
                                    respective rights and interest of any Person
                                    in and to the Proceeds pursuant to this
                                    Article TENTH and applicable law and for
                                    leave to pay the Proceeds into such court.

                           (2) In determining whether any Person has become a
Purported Owner of Excess Shares:

                           (a)      the Corporation is entitled to rely on
                                    Schedule 13D and 13G filings as required by
                                    Rule 13d-1 of the Act to identify the
                                    citizenship of any Person who owns more than
                                    five percent (5%) of the Common Stock; and

                           (b)      in the case of any Person who does not own
                                    more than five percent (5%) of the Common
                                    Stock, without regard to the actual identity
                                    of the ultimate beneficial owners of such
                                    Common Stock, the Corporation may rely on a
                                    statement, signed under oath, or affirmation
                                    by such Person or on the registered address
                                    of such Person to establish the citizenship
                                    of any such Person. The Corporation may not
                                    rely on a statement by such Person or on the
                                    registered address of such Person if the
                                    Corporation knows that the statement is
                                    false.


                                       7
<PAGE>   8

         The Board of Directors shall be fully protected in relying in good
         faith on the items set forth in subparagraphs (a) and (b) of the
         foregoing paragraph (2), together with such other items or sources of
         information as may be required from time to time by the Shipping Act,
         to determine whether any Person has become a Purported Owner of Excess
         Shares.

                  (D) Immediately upon the purported acquisition of any Excess
Shares, the Purported Owner thereof shall give, or cause to be given, written
notice thereof to the Corporation. Each owner of shares of Common Stock shall
furnish to the Corporation all information reasonably requested with respect to
all shares of Common Stock directly and indirectly owned by such Person.

                  (E) Upon a determination by the Board of Directors that a
person has attempted or may attempt to transfer or to acquire Excess Shares, the
Board of Directors may take such action as it deems advisable to refuse to give
effect to such transfer or acquisition on the books and records of the
Corporation, including without limitation, to cause the Transfer Agent to record
the Purported Owner's Transferor as the record owner of the Excess Shares and to
institute proceedings to enjoin or rescind any such transfer or acquisition.

                  (F) If any provision of this Article TENTH or any application
of any such provision is determined to be invalid by any federal or state court
having jurisdiction over the issues, the validity of the remaining provisions
shall not be affected and other application of such provision shall be affected
only to the extent necessary to comply with the determination of such court.

                  (G) It is the purpose of this Article TENTH to facilitate the
Corporation's ability to preserve its ownership by United States citizens as
required under Section 2 of the Shipping Act and to that end the Board of
Directors is authorized to take such action, to the extent permitted by law and
not inconsistent with this Article TENTH, as it may deem necessary or advisable
to protect the Corporation and the interests of the holders of its equity and
debt securities by preservation of the Corporation's ownership by United States
citizens.

                  (H) The Board of Directors may, to the extent permitted by
law, from time to time, establish, modify, amend or rescind, by By-law or
otherwise, regulations and procedures not inconsistent with the express
provisions of this Article TENTH for determining whether any acquisition of
Common Stock would jeopardize the Corporation's ability to maintain such
ownership by citizens of the United States for the orderly application,
administration and implementation of the provisions of this Article TENTH. Such
procedures and regulations shall be kept on file with the Secretary of the
Corporation and with its Transfer Agent and shall be made available for
inspection by the public and, upon request, shall be mailed to any holder of
Common Stock of the Corporation.

                  (I) All certificates evidencing ownership of Common Stock of
the Corporation shall bear a conspicuous legend describing the restriction set
forth in this Article TENTH.

                  ELEVENTH: The Corporation shall not be governed by Section 203
of Delaware General Corporation Law.


                                       8
<PAGE>   9

                  IN WITNESS WHEREOF, American Classic Voyages Co. has caused
this Second Amended and Restated Certificate of Incorporation to be signed by
Jordan B. Allen, its Executive Vice President, General Counsel and Secretary,
and attested by Pam Stringer, its Assistant Secretary, this 29th day of March,
1999.



                                              AMERICAN CLASSIC VOYAGES CO.

                                              By:      /s/ Jordan B. Allen
                                                       ------------------------
                                                       Jordan B. Allen
                                                       Executive Vice President,
                                                       General Counsel and 
                                                       Secretary



Attest:  /s/ Pam Stringer
         ---------------------------------
         Pam Stringer, Assistant Secretary


                                       9