<PAGE>

                                                                     Exhibit 3.1

                              AMENDED AND RESTATED

                                     BYLAWS

                                       OF

                         TIPPINGPOINT TECHNOLOGIES, INC.

<PAGE>

                                TABLE OF CONTENTS

                              AMENDED AND RESTATED
                                     BYLAWS
                                       OF
                         TIPPINGPOINT TECHNOLOGIES, INC.

<TABLE>
<CAPTION>
                                                                                          Page
<S>                                                                                       <C>
ARTICLE I OFFICES                                                                          1
Section 1.        Registered Office                                                        1
                  -----------------
Section 2.        Other Offices                                                            1
                  -------------
ARTICLE II  MEETINGS OF THE STOCKHOLDERS                                                   1
Section 1.        Place of Meetings                                                        1
                  -----------------
Section 2.        Annual Meeting                                                           1
                  --------------
Section 3.        Special Meeting                                                          1
                  ---------------
Section 4.        Notice of Annual or Special Meeting                                      1
                  -----------------------------------
Section 5.        Business at Special Meeting                                              1
                  ---------------------------
Section 6.        Quorum of Stockholders                                                   2
                  ----------------------
Section 7.        Act of Stockholders' Meeting                                             2
                  ----------------------------
Section 8.        Proxies                                                                  2
                  -------
Section 9.        Voting List                                                              2
                  -----------
ARTICLE III  BOARD OF DIRECTORS                                                            3
Section 1.        Powers                                                                   3
                  ------
Section 2.        Compensation of Directors                                                3
                  -------------------------
Section 3.        Chairman of the Board                                                    3
                  ---------------------
ARTICLE IV  MEETINGS OF THE BOARD                                                          3
Section 1.        First Meeting                                                            3
                  -------------
Section 2.        Regular Meetings                                                         3
                  ----------------
Section 3.        Special Meetings                                                         3
                  ----------------
Section 4.        Business at Regular or Special Meeting                                   3
                  --------------------------------------
Section 5.        Quorum of Directors                                                      4
                  -------------------
Section 6.        Act of Directors' Meeting                                                4
                  -------------------------
Section 7.        Action by Unanimous Written Consent Without a Meeting                    4
                  -----------------------------------------------------
ARTICLE V  COMMITTEES                                                                      4
ARTICLE VI  NOTICES                                                                        4
Section 1.        Methods of Giving Notice                                                 4
                  ------------------------
Section 2.        Waiver of Notice                                                         5
                  ----------------
Section 3.        Attendance as Waiver                                                     5
                  -------------------
ARTICLE VII  DIRECTORS' ACTION WITHOUT A MEETING BY USE OF CONFERENCE TELEPHONE            5
ARTICLE VIII OFFICERS                                                                      5
</TABLE>

                                        i

<PAGE>

<TABLE>
<S>                                                                             <C>
Section 1.        Executive Officers                                             5
                  ------------------
Section 2.        Election and Qualification                                     5
                  --------------------------
Section 3.        Salaries                                                       6
                  --------
Section 4.        Term, Removal, and Vacancies                                   6
                  ----------------------------
Section 5.        Chief Executive Officer                                        6
                  -----------------------
Section 6.        President                                                      6
                  ---------
Section 7.        Vice Presidents                                                6
                  ---------------
Section 8.        Secretary                                                      6
                  ---------
Section 9.        Assistant Secretaries                                          6
                  ---------------------
Section 10.       Treasurer                                                      7
                  ---------
Section 11.       Assistant Treasurer                                            7
                  -------------------
Section 12.       Officers' Bond                                                 7
                  --------------
ARTICLE IX CERTIFICATES FOR SHARES                                               7
Section 1.        Certificates Representing Shares                               7
                  --------------------------------
Section 2.        Restriction on Transfer of Shares                              8
                  ---------------------------------
Section 3.        Voting Agreements                                              8
                  -----------------
Section 4.        Transfer of Shares                                             8
                  ------------------
Section 5.        Lost, Stolen, or Destroyed Certificate                         8
                  --------------------------------------
Section 6.        Fixing Record Date                                             9
                  ------------------
Section 7.        Registered Stockholders                                        9
                  -----------------------
ARTICLE X GENERAL PROVISIONS                                                     9
Section 1.        Dividends                                                      9
                  ---------
Section 2.        Reserves                                                       9
                  --------
Section 3.        Negotiable Instruments                                         9
                  ----------------------
Section 4.        Fiscal Year                                                    9
                  -----------
Section 5.        Seal                                                          10
                  ----
Section 6.        Books and Records                                             10
                  -----------------
ARTICLE XI AMENDMENTS                                                           10
</TABLE>

                                       ii

<PAGE>

                              AMENDED AND RESTATED
                                     BYLAWS
                                       OF
                         TIPPINGPOINT TECHNOLOGIES, INC.

                                    ARTICLE I
                                     OFFICES

         Section 1.   Registered Office.  The registered office shall be located
n the City of Wilmington, County of New Castle, State of Delaware.

         Section 2.   Other Offices. The corporation also may have offices at
such other places both within and without the State of Delaware as the Board of
Directors may from time to time determine or as the business of the corporation
may require.

                                   ARTICLE II
                          MEETINGS OF THE STOCKHOLDERS

         Section 1.   Place of Meetings. All meetings of the stockholders for
the election of directors or for any other proper purpose shall be held at such
place either within or without the State of Delaware as the Board of Directors
may from time to time designate, as stated in the notice of such meeting or a
duly executed waiver of notice thereof.

         Section 2.   Annual Meeting. An annual meeting of the stockholders
shall be held at such time and date as the Board of Directors may determine. At
such meeting the stockholders entitled to vote thereat shall elect a Board of
Directors and may transact such other business as properly may be brought before
the meeting.

         Section 3.   Special Meeting. Subject to the rights of the holders of
any series of Preferred Stock, special meetings of the stockholders, unless
otherwise prescribed by statute, may be called at any time only by the Chairman
of the Board of the Corporation or the board of directors pursuant to a
resolution adopted by a majority of the entire board of directors, which
constitutes the total number of directors which the Corporation would have if
there were no vacancies on the board of directors.

         Section 4.   Notice of Annual or Special Meeting. Unless otherwise
required by law, written or printed notice stating the location, day and hour of
the meeting and, in case of a special meeting, the purpose or purposes for which
the meeting is called, shall be delivered not less than ten nor more than 60
days before the date of the meeting, either personally or by mail, by or at the
direction of the Chairman of the Board of the corporation or the Board of
Directors to each stockholder of record entitled to vote at such meeting. If
mailed, such notice shall be deemed to be delivered when deposited in the United
States mail, addressed to the stockholder at his address as it appears on the
stock transfer books of the corporation, with postage thereon prepaid.

         Section 5.   Business at Special Meeting.  The business transacted at
any special meeting of the stockholders shall be limited to the purposes stated
in the notice thereof.

                                       1

<PAGE>

         Section 6.   Quorum of Stockholders. Unless otherwise provided in the
Certificate of Incorporation or applicable law, the holders of a majority of the
shares entitled to vote, represented in person or by proxy, shall constitute a
quorum at a meeting of the stockholders. If, however, a quorum shall not be
present or represented at any meeting of the stockholders, the stockholders
present in person or represented by proxy shall have power to adjourn the
meeting from time to time, without notice other than announcement of location,
day, and hour of the adjourned meeting, until a quorum shall be present or
represented. At such adjourned meeting at which a quorum shall be present or
represented, any business may be transacted which might have been transacted at
the meeting as originally notified, unless the adjournment is for more than 30
days or a new record date is fixed for the adjourned meeting, in which case
notice of the adjourned meeting shall be given to each stockholder of record
entitled to vote at such meeting. The stockholders present at a duly organized
meeting may continue to transact business until adjournment, and the subsequent
withdrawal of any stockholder or the refusal of any stockholder to vote shall
not affect the presence of quorum at the meeting.

         Section 7.   Act of Stockholders' Meeting. Except with respect to the
election of directors, the vote of the holders of a majority of the shares
entitled to vote and represented in person or by proxy at a meeting at which a
quorum is present shall be the act of the stockholders' meeting, unless the vote
of a greater number is required by law or the Certificate of Incorporation.
Unless otherwise provided in the Certificate of Incorporation, directors shall
be elected by a plurality of the votes cast by the holders of shares entitled to
vote in the election of directors at a meeting of stockholders at which a quorum
is present and all elections of directors shall be by written ballot. Where a
separate vote by a class or classes is required, a majority of the outstanding
shares of such class or classes, present in person or represented by proxy,
shall constitute a quorum entitled to take action with respect to that vote on
that matter and the affirmative vote of the majority of shares of such class or
classes present in person or represented by proxy at the meeting shall be the
act of such class.

         Section 8.   Proxies. At any meeting of the stockholders, each
stockholder having the right to vote shall be entitled to vote either in person
or by proxy executed in writing by the stockholder or by his duly authorized
attorney-in-fact. No proxy shall be valid after three (3) years from its date of
execution unless otherwise provided in the proxy. Each proxy shall be revocable
unless expressly provided therein to be irrevocable and the proxy is coupled
with an interest sufficient in law to support an irrevocable proxy or otherwise
made irrevocable by law.

         Section 9.   Voting List. The officer or agent having charge of the
stock ledger of the corporation shall make, at least ten days before each
meeting of the stockholders, a complete list of the stockholders entitled to
vote at such meeting or any adjournment thereof, arranged in alphabetical order,
with the address of and number of shares held by each, which list shall be
maintained, for a period of ten days prior to such meeting, either at a place
within the city where the meeting is to be held, which place shall be specified
in the notice of the meeting, or, if not so specified, at the place where the
meeting is to be held, and shall be subject to inspection by any stockholder at
any time during ordinary business hours. Such list shall also be produced and
kept open at the time and place of the meeting and shall be subject to the
inspection of any stockholder during the whole time of the meeting. The original
stock ledger shall be the only

                                       2

<PAGE>

evidence as to who are the stockholders entitled to examine such list or
transfer books of the corporation or to vote at any such meeting of
stockholders.

                                   ARTICLE III
                               BOARD OF DIRECTORS

         Section 1.   Powers. The business and affairs of the corporation shall
be managed by or under the direction of its Board of Directors, which may
exercise all such powers of the corporation and do all such lawful acts and
things as are not by statute or by the Certificate of Incorporation or by these
Bylaws directed or required to be exercised and done by the stockholders.

         Section 2.   Compensation of Directors. As specifically prescribed from
time to time by resolution of the Board of Directors, the directors of the
corporation may be paid their expenses of attendance at each meeting of the
Board and may be paid a fixed sum for attendance at each meeting of the Board or
a stated compensation for their services in their capacity as directors. This
provision shall not preclude any director from serving the corporation in any
other capacity and receiving compensation therefor. Members of special or
standing committees may be allowed like compensation for attending committee
meetings.

         Section 3.   Chairman of the Board. The Board of Directors, at its
first meeting after each annual meeting of stockholders, may elect one of its
members Chairman of the Board. The Chairman of the Board shall preside at all
meetings of the Board of Directors and shall have such other powers and duties
as usually pertain to such position or as may be delegated by the Board of
Directors.

                                   ARTICLE IV
                             MEETINGS OF THE BOARD

         Section 1.   First Meeting. The first meeting of each newly elected
Board of Directors shall be held immediately following the annual meeting of the
stockholders and no notice of such meeting shall be necessary to the newly
elected directors in order legally to constitute the meeting, provided a quorum
shall be present.

         Section 2.   Regular Meetings. Regular meetings of the Board of
Directors may be held with or without notice at such time and at such place
either within or without the State of Delaware as from time to time shall be
prescribed by the Board of Directors.

         Section 3.   Special Meetings. Special meetings of the Board of
Directors may be called by the Chairman of the Board, the President or by a
majority of the Board of Directors. Written notice of special meetings of the
Board of Directors shall be given to each director at least 24 hours before the
time of the meeting.

         Section 4.   Business at Regular or Special Meeting. Neither the
business to be transacted at nor the purpose of any regular or special meeting
of the Board of Directors need be specified in the notice or waiver of notice of
such meeting.

                                       3

<PAGE>

         Section 5.   Quorum of Directors. A majority of the Board of Directors
shall constitute a quorum for the transaction of business, unless a greater
number is required by law or the Certificate of Incorporation. If a quorum shall
not be present at any meeting of the Board of Directors, the directors present
thereat may adjourn the meeting from time to time, without notice other than
announcement at the meeting, until a quorum shall be present.

         Section 6.   Act of Directors' Meeting.  The act of a majority of the
directors present at a meeting at which a quorum is present shall be the act of
the Board of Directors, unless the act of a greater number is required by law or
the Certificate of Incorporation.

         Section 7.   Action by Unanimous Written Consent Without a Meeting. Any
action required or permitted to be taken at a meeting of the Board of Directors
or any executive committee under the provisions of any applicable law, the
Certificate of Incorporation or these Bylaws may be taken without a meeting if a
consent in writing setting forth the action so taken is signed by all members of
the Board of Directors or of the executive committee, as the case may be, and
such consent is filed with the minutes of proceedings of the Board of Directors
or the executive committee, as the case may be. Such consent shall have the same
force and effect as a unanimous vote of the Board of Directors or of the
executive committee, as the case may be.

                                    ARTICLE V
                                   COMMITTEES

         The Board of Directors, by resolution adopted by a majority of the full
Board of Directors, may designate from among its members an executive committee
and one or more other committees, each of which, to the extent provided in such
resolution or in the Certificate of Incorporation or in these Bylaws, shall have
and may exercise all the authority of the Board of Directors, subject to the
limitations imposed by applicable law. The Board of Directors, by resolution
adopted by a majority of the full Board of Directors, may designate one or more
of its members as alternate members of any committee, who may, subject to any
limitations imposed by the Board of Directors, replace absent or disqualified
members at any meeting of that committee. Vacancies in the membership of any
such committee shall be filled by resolution adopted by the majority of the full
Board of Directors at a regular or special meeting of the Board. All committees
shall keep regular minutes of their proceedings and report the same to the Board
of Directors when required. To the extent applicable, the provisions of Article
IV of these Bylaws governing the meetings of the Board of Directors shall
likewise govern the meetings of any committee thereof. Any member of the
executive committee or any other committee may be removed by the Board of
Directors by the affirmative vote of a majority of the full Board, whenever, in
its judgment, the best interests of the corporation will be served thereby.

                                   ARTICLE VI
                                     NOTICES

         Section 1.   Methods of Giving Notice. Whenever any notice is required
to be given to any stockholder or director under the provisions of any law, the
Certificate of Incorporation or these Bylaws, it shall be given in writing and
delivered personally or mailed to such stockholder or director at such address
as appears on the books of the corporation, and such notice shall be deemed to
be given at the time the same shall be deposited in the United States mail with

                                       4

<PAGE>

sufficient postage thereon prepaid. Notice to directors may also be given by
telegram, telex, telecopy, or similar means of visual data transmission, and
notice given by any of such means shall be deemed to be delivered when
transmitted for delivery to the recipient.

         Section 2.   Waiver of Notice. Whenever any notice is required to be
given to any stockholder or director under the provisions of any law, the
Certificate of Incorporation, or these Bylaws, a waiver thereof in writing
signed by the person or persons entitled to said notice, whether before or after
the time stated therein, shall be deemed equivalent to the giving of such
notice.

         Section 3.   Attendance as Waiver. Attendance of a stockholder or
director at a meeting shall constitute a waiver of notice of such meeting,
except where a stockholder or director attends a meeting for the express purpose
of objecting, at the beginning of the meeting, to the transaction of any
business on the ground that the meeting is not lawfully called or convened.
Neither the business to be transacted at, nor the purpose of, a meeting need be
specified in any written waiver unless required by the Certificate of
Incorporation or these Bylaws.

                                   ARTICLE VII
                DIRECTORS' ACTION BY USE OF CONFERENCE TELEPHONE

         Subject to the provisions required or permitted for notice of meetings,
unless otherwise restricted by the Certificate of Incorporation or these Bylaws,
members of the Board of Directors or members of any committee designated by such
Board of Directors may participate in and hold a meeting of such Board of
Directors or committee by conference telephone or similar communications
equipment by means of which all persons participating in the meeting can hear
each other, and participation in such a meeting shall constitute presence in
person at such meeting, except where a person participates in the meeting for
the express purpose of objecting, at the beginning of the meeting, to the
transaction of any business on the ground that the meeting is not lawfully
called or convened.

                                  ARTICLE VIII
                                    OFFICERS

         Section 1.   Executive Officers. The officers of the corporation shall
consist of a President and a Secretary and may also include one or more Vice
Presidents, a Treasurer, and such other officers as are provided for in this
Article VIII, each of whom shall be elected by the Board of Directors as
provided in Section 2 of this Article. Any two (2) or more offices may be held
by the same person.

         Section 2.   Election and Qualification. The Board of Directors, at its
first meeting held immediately after each annual meeting of stockholders, shall
choose a President and a Secretary. The Board of Directors also may elect one or
more Vice Presidents, a Treasurer, and such other officers, including assistant
officers and agents as may be deemed necessary, who shall hold their offices for
such terms and shall exercise such powers and perform such duties as shall be
determined from time to time by the Board of Directors.

                                       5

<PAGE>

         Section 3.   Salaries.  The compensation of all officers and agents of
the corporation shall be determined by the Board of Directors.

         Section 4.   Term, Removal, and Vacancies. Each officer of the
corporation shall hold office until his successor is chosen and qualified or
until his death, resignation, or removal. Any officer may resign at any time
upon giving written notice to the corporation. Any officer or agent or member of
the executive committee elected or appointed by the Board of Directors may be
removed by the Board of Directors with or without cause, but such removal shall
be without prejudice to the contract rights, if any, of the person so removed.
Election or appointment of an officer or agent shall not of itself create
contract rights. Any vacancy occurring in any office of the corporation by
death, resignation, removal, or otherwise shall be filled by the Board of
Directors.

         Section 5.   Chief Executive Officer. Unless the Board of Directors
designates otherwise, the President shall be the Chief Executive Officer of the
corporation. The Chief Executive Officer shall preside at all meetings of the
stockholders. The Chief Executive Officer shall have such other powers and
duties as usually pertain to such office or as may be delegated by the Board of
Directors.

         Section 6.   President. The President shall, subject to the oversight
and the direction of the Board of Directors, have general powers of oversight,
supervision, and management of the business and affairs of the corporation, and
shall see that all orders and resolutions of the Board of Directors are carried
into effect. The President shall have such other powers and duties as usually
pertain to such office or as may be prescribed by the Board of Directors. The
President shall execute bonds, mortgages, instruments, contracts, agreements,
and other documentation, except where the signing and execution thereof shall be
expressly delegated by the Board of Directors to some other officer or agent of
the corporation.

         Section 7.   Vice Presidents. Unless otherwise determined by the Board
of Directors, the Vice Presidents, in the order of their seniority as such
seniority may from time to time be designated by the Board of Directors, shall
perform the duties and exercise the powers of the President in the absence or
disability of the President. They shall perform such other duties and have such
other powers as the Board of Directors may from time to time prescribe.

         Section 8.   Secretary. The Secretary shall attend all meetings of the
Board of Directors and all meetings of the stockholders, shall record all the
proceedings of the meetings of the stockholders and of the Board of Directors in
books to be kept for that purpose, and shall perform like duties for the
standing committees when required. The Secretary shall give, or cause to be
given, notice of all meetings of the stockholders and special meetings of the
Board of Directors, and shall perform such other duties as may be prescribed by
the Board of Directors. The Secretary shall keep in safe custody the seal of the
corporation, and, when authorized by the Board of Directors, affix the same to
any instrument requiring it. When so affixed, such seal shall be attested by his
or her signature or by the signature of the Treasurer or an Assistant Secretary.

         Section 9.   Assistant Secretaries.  Unless otherwise determined by the
Board of Directors, the Assistant Secretaries, in the order of their seniority
as such seniority may from

                                       6

<PAGE>

time to time be designated by the Board of Directors, shall perform the duties
and exercise the powers of the Secretary in the absence or disability of the
Secretary. They shall perform such other duties and have such other powers as
the Board of Directors may from time to time prescribe.

         Section 10.  Treasurer. The Treasurer shall have the custody of the
corporate funds and securities and shall keep full and accurate accounts of
receipts and disbursements in books belonging to the corporation and shall
deposit all moneys and other valuable effects in the name and to the credit of
the corporation in such depositories as may be designated by the Board of
Directors. The Treasurer shall disburse the funds of the corporation as may be
ordered by the Board of Directors, taking proper vouchers for such
disbursements, and shall perform such other duties and have such other powers as
the Board of Directors may from time to time prescribe.

         Section 11.  Assistant Treasurer. Unless otherwise determined by the
Board of Directors, the Assistant Treasurer shall perform the duties and
exercise the powers of the Treasurer in the absence or disability of the
Treasurer. The Assistant Treasurer shall perform such other duties and have such
other powers as the Board of Directors may from time to time prescribe.

         Section 12.  Officers' Bond. If required by the Board of Directors, any
officer so required shall give the corporation a bond, which shall be renewed as
the Board of Directors may require, in such sum and with such surety or sureties
as shall be satisfactory to the Board of Directors for the faithful performance
of the duties of his or her office and for the restoration to the corporation,
in case of his or her death, resignation, retirement or removal from office, of
any and all books, papers, vouchers, money and other property of whatever kind
in his or her possession or under his or her control belonging to the
corporation.

                                   ARTICLE IX
                             CERTIFICATES FOR SHARES

         Section 1.   Certificates Representing Shares. The corporation shall
deliver certificates representing all shares to which stockholders are entitled.
Such certificates shall be numbered and shall be entered in the books of the
corporation as they are issued, and shall be signed by the Chairman of the Board
of Directors, the President or a Vice President, and by the Treasurer or an
Assistant Treasurer, or the Secretary or an Assistant Secretary of the
corporation, and may be sealed with the seal of the corporation or a facsimile
thereof. Any or all signatures on the certificate may be a facsimile. In case
any officer who has signed or whose facsimile signature has been placed upon
such certificate shall have ceased to be such officer before such certificate is
issued, it may be issued by the corporation with the same effect as if he or she
were such officer at the date of its issuance. If the corporation is authorized
to issue shares of more than one class, there shall be set forth upon the face
or back of the certificate a statement that the corporation will furnish to any
stockholder upon request and without charge a full statement of all of the
powers, designations, preferences, limitations and relative, participating,
optional, or other special rights of the shares of each class authorized to be
issued and the qualifications, limitations or restrictions of such preferences
and/or rights and, if the corporation is authorized to issue any preferred or
special class in series, the variations in the relative rights and preferences
between the shares of each such series so far as the same have been fixed and
determined and the

                                       7

<PAGE>

authority of the Board of Directors to fix and determine the relative rights and
preferences of subsequent series. Each certificate representing shares shall
state upon the face thereof that the corporation is organized under the laws of
the State of Delaware, the name of the person to whom issued, the number and the
class and the designation of the series, if any, which such certificate
represents and the par value of each share represented by such certificate or a
statement that the shares are without par value. No certificate shall be issued
for any share until the consideration therefor has been fully paid.

         Section 2.   Restriction on Transfer of Shares. If any restriction on
the transfer, or registration of the transfer, of shares shall be imposed or
agreed to by the corporation, as permitted by law, the Certificate of
Incorporation, or these Bylaws, such restriction shall be noted conspicuously on
each certificate representing shares in accordance with applicable law.

         Section 3.   Voting Agreements. A written counterpart of any voting
agreement entered into among any number of stockholders of the corporation, or
any number of stockholders of the corporation and the corporation itself, for
the purpose of providing that shares of the corporation shall be voted in the
manner prescribed in the agreement shall be deposited with the corporation at
its registered office in Delaware and shall be subject to the inspection by any
stockholder of the corporation or any beneficiary of the agreement daily during
business hours. In addition, certificates of stock or uncertificated stock shall
be issued to the person or persons or corporation or corporations authorized to
act as trustee for purposes of vesting in such person or persons, corporation or
corporations the right to vote such shares, to represent any stock of an
original issue so deposited with the trustee or trustees, and any certificates
of stock or uncertificated stock so transferred to the voting trustee or
trustees shall be surrendered and cancelled and new certificates or
uncertificated stock shall be issued therefore to the voting trustee or
trustees. In the certificate so issued, if any, it shall be stated that it is
issued pursuant to such agreement, and that fact shall also be stated in the
stock ledger of the corporation.

         Section 4.   Transfer of Shares. Subject to the provisions of Section 7
of this Article IX, upon surrender to the corporation or the transfer agent of
the corporation of a certificate for shares duly endorsed or accompanied by
proper evidence of succession, assignment, or authority to transfer, it shall be
the duty of the corporation to issue a new certificate to the person entitled
thereto, cancel the old certificate, and record the transaction upon its books.

         Section 5.   Lost, Stolen, or Destroyed Certificate. The Board of
Directors may direct a new certificate or certificates to be issued in place of
any certificate or certificates theretofore issued by the corporation alleged to
have been lost, stolen, or destroyed upon the making of an affidavit of that
fact by the person claiming the certificate to be lost, stolen or destroyed.
When authorizing such issue of a new certificate or certificates, the Board of
Directors, in its discretion and as a condition precedent to the issuance
thereof, may require the owner of such lost, stolen or destroyed certificate or
certificates, or his legal representative, to advertise the same in such manner
as it shall require and/or to give the corporation a bond in such sum as it may
direct to indemnify the corporation against any claim that may be made against
the corporation with respect to the certificate alleged to have been lost,
stolen or destroyed or the issuance of such new certificate.

                                       8

<PAGE>

         Section 6.   Fixing Record Date. For the purpose of determining
stockholders entitled to notice of or to vote at any meeting of stockholders or
any adjournment thereof, or entitled to receive payment of any dividend or other
distribution, or in order to make a determination of stockholders for any other
proper purpose, the Board of Directors may fix a date as the record date for any
such determination of stockholders, such date to not precede the date of
adoption of the resolution fixing the record date, and such date to be not more
than 60 days, and, in case of a meeting of stockholders, not less than ten days,
prior to the date on which the particular action requiring such determination of
stockholders is to be taken. If no record date is fixed for the determination of
stockholders entitled to notice of or to vote at a meeting of stockholders, or
stockholders entitled to receive payment of a dividend or other distribution, or
for any other proper purpose, the close of business on the day next preceding
the date on which notice of the meeting is mailed or if notice is waived, the
close of business on the day next preceding the day on which the meeting is held
or the date on which the resolution of the Board of Directors declaring such
dividend or relating to such other proper purpose is adopted, as the case may
be, shall be the record date for such determination of stockholders. When a
determination of stockholders entitled to vote at any meeting of stockholders
has been made as provided in this Section 6, such determination shall apply to
any adjournment thereof; provided that the Board of Directors may fix a new
record date for the adjourned meeting.

         Section 7.   Registered Stockholders. The corporation shall be entitled
to recognize the exclusive right of a person registered on its books as the
owner of shares to receive dividends, and to vote as such owner, and shall not
be bound to recognize any equitable or other claim to or interest in such share
or shares on the part of any other person, whether or not it shall have express
or other notice thereof, except as otherwise provided by the laws of the State
of Delaware.

                                    ARTICLE X
                               GENERAL PROVISIONS

         Section 1.   Dividends. The Board of Directors from time to time may
declare, and the corporation may pay, dividends on its outstanding shares in
cash, property, or its own shares pursuant to law and subject to the provisions
of the Certificate of Incorporation and these Bylaws.

         Section 2.   Reserves. The Board of Directors may by resolution create
a reserve or reserves out of earned surplus for any proper purpose or purposes,
and may abolish any such reserve in the same manner.

         Section 3.   Negotiable Instruments. All bills, notes, checks, or
instruments for the payment of money shall be signed by such officer or officers
or such other person or persons as permitted by these Bylaws or in such manner
as the Board of Directors from time to time may designate.

         Section 4.   Fiscal Year.  The fiscal year of the corporation shall be
fixed by resolution of the Board of Directors.

                                       9

<PAGE>


         Section 5.   Seal.  The corporate seal shall have inscribed thereon the
name of the corporation and may be used by causing it or a facsimile thereof to
be impressed or affixed or in any other manner reproduced.

         Section 6.   Books and Records. The corporation shall keep books and
records of account and shall keep minutes of the proceedings of the
stockholders, the Board of Directors, and each committee of the Board of
Directors. The corporation shall keep at its registered office or principal
place of business, or at the office of its transfer agent or registrar, a record
of the original issuance of shares issued by the corporation and a record of
each transfer of those shares that have been presented to the corporation for
registration of transfer. Such records shall contain the names and addresses of
all past and current stockholders of the corporation and the number and class of
shares issued by the corporation held by each of them. Any books, records,
minutes, and share transfer records may be in written form or in any other form
capable of being converted into written form within a reasonable time.

                                   ARTICLE XI
                                   AMENDMENTS

         These Bylaws may be amended or repealed or new bylaws adopted as
provided by the Certificate of Incorporation.

                            CERTIFICATE OF SECRETARY

         The undersigned hereby certifies that (i) he is the duly elected and
qualified Secretary of TippingPoint Technologies, Inc., a Delaware corporation
(the "Company"), and (ii) the foregoing is a true and correct copy of the
Amended and Restated Bylaws of the Company reviewed and adopted by the Board of
Directors of the Company.

                                            /s/ JAMES E. CAHILL
                                            ____________________________________
                                            James E. Cahill, Secretary

                                            August 22, 2002
                                            ____________________________________
                                            Date

                                       10