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Exhibit 3.1 AMENDED AND RESTATED
CERTIFICATE OF INCORPORATION
OF
AMERICAN MEDICAL SYSTEMS HOLDINGS, INC. [Composite as amended through March 4, 2005] ARTICLE I. The name of the corporation is: American Medical Systems Holdings, Inc. (the Corporation). ARTICLE II. The address of its registered office in the State of Delaware is 1209 Orange Street in the
City of Wilmington, County of New Castle. The name of its registered agent at such address is The
Corporation Trust Company. ARTICLE III. The nature of the business or purposes to be conducted or promoted by the Corporation is to
engage in any lawful act or activity for which corporations may be organized under the General
Corporation Law of the State of Delaware. ARTICLE IV. The total authorized capital stock of the Corporation shall be Two Hundred Twenty-five Million
(225,000,000) shares consisting of (i) Two Hundred Million (200,000,000) shares of Common Stock,
$.01 par value per share (Voting Common Stock); (ii) Twenty Million (20,000,000) shares of
Non-Voting Common Stock, $.01 par value per share (Non-Voting Common Stock, and together with the
Voting Common Stock, Common Stock); and (iii) Five Million (5,000,000) shares of Preferred Stock,
$.01 par value per share (Preferred Stock).  (a)
    Common Stock. (i) Ranking. Except with respect to voting rights and the conversion rights of
the Non-Voting Common Stock, the Voting Common Stock and the Non-Voting Common Stock shall
in all respects have the same powers, rights and qualifications (including, relative,
participating, optional and other special rights, dividend rights and rights on liquidation,
dissolution or winding up) and shall rank pari passu with each other. (ii) Dividends. Subject to the preferences and other rights of the Preferred
Stock, if any, the holders of Common Stock shall be entitled to receive dividends when and
as declared by the Board of Directors out of funds legally available therefor. Holders of
shares of Voting Common Stock and Non-Voting Common Stock shall be entitled to share
equally, share for share, in such dividends, except that if dividends are declared which are
payable in shares of Voting Common Stock or Non-Voting Common Stock, dividends shall be
declared which are payable at the same rate in both classes of stock and the dividends
payable in shares of Voting Common Stock shall be payable to the holders of that class of
stock and the dividends payable in shares of Non-Voting Common Stock shall be payable to the
holders of that class of stock. (iii) Liquidation. In the event of any liquidation, dissolution or winding up
of the affairs of the Corporation, voluntary or involuntary, after payment or provision for
payment to the holders of the Corporations Preferred Stock of the amounts to which they may
be entitled as set out above, the remaining assets 1




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of the Corporation available to stockholders shall be distributed equally per
share to the holders of Common Stock irrespective of class. (iv) Voting. (A) Voting Common Stock. Except as otherwise provided herein or by law,
each holder of Voting Common Stock shall be entitled to one vote in respect of each
share of Voting Common Stock held of record on all matters submitted to a vote of
stockholders. (B) Non-Voting Common Stock. (1) Except as required by law or by paragraph (a)(iv)(B)(3) below, the
holders of Non-Voting Common Stock shall not be entitled to vote on any
matters to be voted on by the stockholders of the Corporation. (2) Notwithstanding paragraph (a)(iv)(B)(1) above the holders of the
Non-Voting Common Stock shall be entitled to the same notice of meetings of
stockholders as the holders of the Voting Common Stock. (3) The Corporation shall not (y) amend, alter or repeal paragraphs
(a)(ii) or (a)(iii) if such amendment, alteration or repeal would cause the
Voting Common Stock to obtain a liquidation preference or right or a dividend
preference or right more favorable than that of the Non-Voting Common Stock or
(z) amend, alter or repeal paragraphs (a)(i) or (a)(v), in either case without
the approval of the holders of at least a majority of the then outstanding
aggregate number of shares of Non-Voting Common Stock (with each share of
Non-Voting Common Stock entitled to one vote), given in writing or by vote at
a meeting, with the Non-Voting Common Stock consenting or voting (as the case
may be) together as a single class. (v) Conversion of Non-Voting Common Stock. (A) Each holder of Non-Voting Common Stock shall, at such holders option, be
entitled to convert into an equal number of fully paid and nonassessable shares of
Voting Common Stock any or all of the shares of such holders Non-Voting Common
Stock; provided that (i) any Conversion Event (as defined in paragraph (a)(v)(B)
below) shall have occurred (or is expected to occur as described in paragraph
(a)(v)(D) below), in which case, such holder shall be entitled to convert any or all
of the shares of such holder being (or expected to be) distributed, disposed of or
sold in connection with such Conversion Event or (ii) the holder thereof delivers to
the Corporation, together with the notice of election and the applicable stock
certificates, a certificate of such holder to the effect that (x) such holder is a
person other than Warburg, Pincus Equity Partners, L.P. (WPEP) or any affiliate (as
defined in Rule 12b-2 promulgated under the Securities Exchange Act of 1934, as
amended (the Exchange Act) or any successor rule) of WPEP, or (y) if such holder is
WPEP, upon such conversion and giving effect thereto, such holder and all affiliates
of such holder will collectively own beneficially of record no more than fifty
percent (50%) of the then outstanding shares of Voting Common Stock (it being
understood that the provisions of this clause (y) shall apply in the case of a
contemporaneous conversion and distribution by WPEP to its partners where the shares
so converted are registered in the names of such partners). The Corporation or its
transfer agent shall rely on any such certificate as accurately setting forth the
facts therein stated, unless the Corporation has actual knowledge of the falseness of
any such statements of fact. (B) For purposes of this paragraph (a)(v), a Conversion Event shall mean (w)
any sale in connection with any public offering or public sale of securities of the
Corporation (including a public offering registered under the Securities Act and a
public sale pursuant to Rule 144 of the Securities and Exchange Commission thereunder
or any similar rule then in force), (x) any sale
(including by way of merger, consolidation or other similar transaction) of
securities of the Corpora- 2




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tion to a
person or group of persons (within the meaning of the Exchange Act)
if, after such sale, such person or group of persons, in the
aggregate, would own or control securities which possess in the aggregate the
ordinary voting power to elect a majority of the Corporations directors (provided
that such sale has been approved by the Board of Directors or a committee thereof),
(y) any sale (including by way of merger, consolidation or other similar transaction)
of securities of the Corporation to a person or group of persons (within the meaning
of the Exchange Act) if, after such sale, such person or group of persons in the
aggregate would own or control securities of the Corporation (excluding any shares of
Non-Voting Common Stock being converted and disposed of in connection with such
Conversion Event) which possess, in the aggregate, the ordinary voting power to elect
a majority of the Corporations directors, and (z) any sale of securities of the
Corporation to a person or group of persons (within the meaning of the Exchange Act)
if, after such sale, such person or group of persons would not, in the aggregate,
own, control or have the right to acquire more than two percent (2%) of the
outstanding securities of any class of voting securities of the Corporation. For
purposes of this paragraph 3(e)(ii), a person shall include any natural person and
any corporation, partnership, joint venture, trust, unincorporated organization and
any other entity or organization. (C) Each holder of Non-Voting Common Stock shall be entitled to convert shares
of Non-Voting Common Stock which are to be distributed, disposed of or sold in
connection with any Conversion Event if such holder reasonably believes that such
Conversion Event will be consummated. The Corporation will not retire the shares of
Non-Voting Common Stock so converted before the tenth day following such Conversion
Event and will reserve such shares until such tenth day for reissuance in compliance
with the next sentence. If any shares of Non-Voting Common Stock are converted into
shares of Voting Common Stock in connection with a Conversion Event and such shares
of Voting Common Stock are not actually distributed, disposed of or sold pursuant to
such Conversion Event, such shares of Voting Common Stock shall be promptly converted
back into the same number of shares of Non-Voting Common Stock. (D) In order to exercise the conversion privilege in this paragraph (a)(v), a
holder of Non-Voting Common Stock shall surrender to the Corporation at its principal
offices, or to any transfer agent for the Corporation, a certificate or certificates
for Non-Voting Common Stock to be converted together with (y) a certificate of such
holder stating such holders reasonable belief that such holder is entitled to
convert pursuant to the terms hereof (which certificate shall be conclusive and shall
obligate the Corporation to effect such conversion in a timely manner) (a Conversion
Eligibility Certificate) and (z) a written notice to the Corporation that such
holder has elected to convert such shares, or, if less than all shares represented by
such certificate are to be converted, the portion of the shares represented thereby
to be converted. Such notice shall also state the name or names (with addresses) in
which the certificates for shares of Voting Common Stock issuable upon such
conversion shall be issued, subject to any restrictions on transfer relating to
shares of Non-Voting Common Stock or shares of Voting Common Stock issuable upon
conversion thereof. If so required by the Corporation, certificates surrendered for
conversion shall be endorsed or accompanied by written instrument or instruments of
transfer, in form satisfactory to the Corporation, duly authorized in writing.
Non-Voting Common Stock shall be deemed converted for all purposes including without
limitation the taking of a record date for a meeting of the stockholders of the
Corporation, upon receipt by the Corporation or its transfer agent of such
certificates evidencing such shares accompanied by a Conversion Eligibility
Certificate and such notice of election to convert. (E) If any certificate evidencing Non-Voting Common Stock surrendered to the
Corporation for conversion evidences shares of Non-Voting Common Stock in addition to
the shares of Non-Voting Common Stock being so converted, then following such
conversion, the Corporation shall cause to be executed and delivered to the holder
thereof, at the expense of the Corporation, a new certificate evidencing the balance
of the Non-Voting Common Stock that was not so converted. (F) The Corporation shall at all times reserve and keep available out of its
authorized but unissued Voting Common Stock the full number of shares
of such stock into which all authorized 3




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shares of Non-Voting Common Stock are convertible solely
for the purpose of effecting the conversion of the shares of Non-Voting Common Stock;
and if at any time the number of authorized but unissued shares of Voting Common
Stock shall not be sufficient to effect the conversion of all then authorized shares
of Non-Voting Common Stock, the Corporation will take such corporate action as may,
in the opinion of its counsel, be necessary to increase its authorized but unissued
shares of Voting Common Stock, to such number of shares as shall be sufficient for
such purpose, including without limitation, engaging in best efforts to obtain the
requisite stockholder approval of any necessary amendment to this Certificate of
Incorporation. (vi) Reclassifications. The Corporation shall not effect any stock split or
division, reverse stock split, stock dividend, reclassification, reorganization,
combination, recapitalization or consolidation of either class of Common Stock, unless the
Corporation shall also contemporaneously effect a stock split or division, reverse stock
split, stock dividend, reclassification, reorganization, combination or consolidation on the
same terms with respect to the other class of Common Stock; provided, that in any
such transaction, only holders of Voting Common Stock shall receive shares of Voting Common
Stock and only holders of Non-Voting Common Stock shall receive shares of Non-Voting Common
Stock. (b) Preferred Stock. The Preferred Stock may be issued from time to time in one or
more series, each of which series shall have such distinctive designation or title and such number
of shares as shall be fixed by the Board of Directors prior to the issuance of any shares thereof.
Each such series of Preferred Stock shall have such voting powers, full or limited, or no voting
powers, and such preferences and relative, participating, optional or other special rights and such
qualifications, limitations or restrictions thereof, as shall be stated and expressed in the
resolution or resolutions providing for the issue of such series of Preferred Stock as may be
adopted from time to time by the Board of Directors prior to the issuance of any shares thereof
pursuant to the authority hereby expressly vested in it. The Board of Directors is further
authorized to increase or decrease (but not below the number of shares outstanding) the number of
shares of any series of Preferred Stock subsequent to the issuance of shares of that series. In
case the number of shares of any series shall be so decreased, the shares constituting such
decrease shall resume the status of which they had prior to the adoption of the resolution
originally fixing the number of shares of such series. Except as provided in the resolution or
resolutions of the Board of Directors creating any series of Preferred Stock, the shares of Common
Stock shall have the exclusive right to vote for the election and removal of directors and for all
other purposes. Each holder of Common Stock shall be entitled to one vote for each share held. ARTICLE V. In furtherance and not in limitation of the powers conferred by statute, the By-Laws of the
Corporation may be made, altered, amended or repealed by the stockholders or by a majority of the
entire Board of Directors. ARTICLE VI. Whenever a compromise or arrangement is proposed between this Corporation and its creditors or
any class of them and/or between this Corporation and its stockholders or any class of them, any
court of equitable jurisdiction within the State of Delaware may, on the application in a summary
way of this Corporation or of any creditor or stockholder thereof or on the application of any
receiver or receivers appointed for this Corporation under the provisions of Section 291 of Title 8
of the Delaware Code or on the application of trustees in dissolution or of any receiver or
receivers appointed for this Corporation under the provisions of Section 279 of Title 8 of the
Delaware Code order a meeting of the creditors or class of creditors, and/or of the stockholders or
class of stockholders of this Corporation, as the case may be, to be summoned in such manner as the
said court directs. If a majority in number representing three fourths in value of the creditors
or class of creditors, and/or of the stockholders or class of stockholders of this Corporation, as
the case may be, agree to any compromise or arrangement and to any reorganization of this
Corporation as consequence of such compromise or arrangement, the said compromise or arrangement,
the said compromise or arrangement and the said reorganization shall, if sanctioned by the court to
which the said application has been made, be binding on all the creditors or class of creditors,
and/or on all stockholders or class of stockholders of this Corporation, as the case may be, and
also on this Corporation. 4




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ARTICLE VII. Elections of directors need not be by written ballot. ARTICLE VIII. (a) The Corporation shall indemnify to the fullest extent authorized or permitted under and in
accordance with the laws of the State of Delaware (as now or hereafter in effect) any person who
was or is a 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 by reason of
the fact that he or she 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, trustee, employee or agent
of or in any other capacity with another corporation, partnership, joint venture, trust or other
enterprise, against expenses (including attorneys fees), judgments, fines and amounts paid in
settlement actually and reasonably incurred by him or her in connection with such action, suit or
proceeding if he or she acted in good faith and in a manner he or she reasonably believed to be in
or not opposed to the best interests of the Corporation, and, with respect to any criminal action
or proceeding, had no reasonable cause to believe his or her conduct was unlawful. (b) Expenses incurred in defending a civil or criminal action, suit or proceeding shall (in
the case of any action, suit or proceeding against a director of the Corporation) or may (in the
case of any action, suit or proceeding against an officer, trustee, employee or agent) be paid by
the Corporation in advance of the final disposition of such action, suit or proceeding as
authorized by the Board of Directors upon receipt of an undertaking by or on behalf of the
indemnified person to repay such amount if it shall ultimately be determined that he or she is not
entitled to be indemnified by the Corporation as authorized in this Article. (c) The indemnification and other rights set forth in this Article shall not be exclusive of
any provisions with respect thereto in the By-Laws or any other contract or agreement between the
Corporation and any officer, director, employee or agent of the Corporation. (d) Neither the amendment nor repeal of paragraph (a), (b) or (c), nor the adoption of any
provision of this Amended and Restated Certificate of Incorporation inconsistent with paragraph
(a), (b) or (c), shall eliminate or reduce the effect of paragraphs (a), (b) and (c), in respect of
any matter occurring before such amendment, repeal or adoption of an inconsistent provision or in
respect of any cause of action, suit or claim relating to any such matter which would have given
rise to a right of indemnification or right to receive expenses pursuant to paragraph (a), (b) or
(c), if such provision had not been so amended or repealed or if a provision inconsistent therewith
had not been so adopted. (e) No director shall be personally liable to the Corporation or any stockholder for monetary
damages for breach of fiduciary duty as a director, except for any matter in respect of which such
director (a) shall be liable under Section 174 of the General Corporation Law of the State of
Delaware or any amendment thereto or successor provision thereto, or (b) shall be liable by reason
that, in addition to any and all other requirements for liability, he or she: (i) shall have breached his or her duty of loyalty to the Corporation or its
stockholders; (ii) shall not have acted in good faith or, in failing to act, shall not have acted
in good faith; (iii) shall have acted in a manner involving intentional misconduct or a knowing
violation of law or, in failing to act, shall have acted in a manner involving intentional
misconduct or a knowing violation of law; or (iv) shall have derived an improper personal benefit. If the General Corporation Law of the State of Delaware is amended after the date of this
Amended and Restated Certificate of Incorporation to authorize corporate action further eliminating
or limiting the personal liabil 5




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ity of directors, then the liability of a director of the
Corporation shall be eliminated or limited to the fullest extent permitted by the General
Corporation Law of the State of Delaware, as so amended. ARTICLE IX The number of directors which shall constitute the entire Board of Directors shall not be less
than one (1) nor more than nine (9), which number shall be determined from time to time by the
Board of Directors. The Directors shall be divided into three (3) classes, as nearly equal in
number as possible. The term of office of the first class shall expire at the 2001 annual meeting
of the stockholders of the Corporation; the term of office of the second class shall expire at the
2002 annual meeting of the stockholders of the Corporation; and the term of office of the third
class shall expire at the 2003 annual meeting of the stockholders of the Corporation. At each
annual meeting of the stockholders after such classification, the number of directors equal to the
number of the class whose term expires on the day of such meeting shall be elected for a term of
three (3) years. Directors shall hold office until expiration of the terms for which they were
elected and qualified; provided, however, that a director may be removed from office as a director
at any time by the stockholders, but only for cause, and only by the affirmative vote of a majority
of the outstanding voting power entitled to elect such director. If the office of any director
becomes vacant by reason of death, resignation, retirement, disqualification, removal from office,
increase in the number of directors or otherwise, a majority of the remaining directors, although
less than a quorum, at a meeting called for that purpose, may choose a successor, who, unless
removed for cause as set forth above, shall hold office until the expiration of the term of the
class for which appointed or until a successor shall be elected and qualified. This Article IX may
not be altered, amended or repealed, in whole or in part, unless authorized by the affirmative vote
of the holders of not less than two-thirds of the outstanding voting power entitled to vote. ARTICLE X. The Corporation reserves the right to amend, alter, change, or repeal any provisions contained
in this Amended and Restated Certificate of Incorporation in the manner now or hereafter prescribed
by statute, and all rights conferred upon stockholders herein are granted subject to this
reservation. 6