<PAGE>

                                                                     EXHIBIT 4.1

                          SECOND AMENDED AND RESTATED

                         CERTIFICATE OF INCORPORATION

                                      OF

                         CYPRESS COMMUNICATIONS, INC.

     CYPRESS COMMUNICATIONS, INC., a corporation organized and existing under
the laws of the State of Delaware (the "Corporation"), hereby certifies as
follows:

     1.   The name of the Corporation is Cypress Communications, Inc. The date
of the filing of its original Certificate of Incorporation with the Secretary of
State of the State of Delaware was July 15, 1997.

     2.   This Second Amended and Restated Certificate of Incorporation (the
"Certificate") amends, restates and integrates the provisions of the Amended and
Restated Certificate of Incorporation that was filed with the Secretary of State
of the State of Delaware on September 30, 1998, as heretofore amended (the
"Amended and Restated Certificate"), and was duly adopted in accordance with the
provisions of Sections 242 and 245 of the Delaware General Corporation Law (the
"DGCL").

     3.   The text of the Amended and Restated Certificate is hereby amended and
restated in its entirety to provide as herein set forth in full.

                                   ARTICLE I

     The name of the Corporation is Cypress Communications, Inc.

                                  ARTICLE II

     The address of the Corporation's registered office in the State of Delaware
is c/o The Corporation Trust Company, 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 purpose of the Corporation is to engage in any lawful act or activity
for which corporations may be organized under the DGCL.
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                                  ARTICLE IV

                                 CAPITAL STOCK
                                 -------------

     The total number of shares of capital stock which the Corporation shall
have authority to issue is One Hundred Seventy-One Million (171,000,000) shares,
of which (i) One Hundred Fifty Million (150,000,000) shares shall be a class
designated as common stock, par value $.001 per share (the "Common Stock"), (ii)
One Million (1,000,000) shares shall be a class designated as Series Z Junior
Participating Cumulative Preferred Stock, par value $.001 per share (the "Series
Z Preferred Stock"), and (iii) Twenty Million (20,000,000) shares shall be a
class designated as undesignated preferred stock, par value $.001 per share (the
"Undesignated Preferred Stock"). The Series Z Preferred Stock and the
Undesignated Preferred Stock are sometimes collectively referred to herein as
the "Preferred Stock."

     The number of authorized shares of the class of Undesignated Preferred
Stock may from time to time be increased or decreased (but not below the number
of shares outstanding) by the affirmative vote of the holders of a majority of
the outstanding shares of Common Stock entitled to vote, without a vote of the
holders of the Preferred Stock (subject to the terms of the Series Z Preferred
Stock and except as otherwise provided in any certificate of designations of any
series of Undesignated Preferred Stock).

     The powers, preferences and rights of, and the qualifications, limitations
and restrictions upon, each class or series of stock shall be determined in
accordance with, or as set forth below in, this Article IV.

                               A.  COMMON STOCK
                                   ------------

          Subject to all the rights, powers and preferences of the Preferred
Stock and except as provided by law or in this Article IV (or in any certificate
of designations of any series of Undesignated Preferred Stock):

               (a)  the holders of the Common Stock shall have the exclusive
right to vote for the election of directors of the Corporation ("Directors") and
on all other matters requiring stockholder action, each outstanding share
entitling the holder thereof to one vote on each matter properly submitted to
the stockholders of the Corporation for their vote; provided, however, that,
                                                    --------  -------
except as otherwise required by law, holders of Common Stock, as such, shall not
be entitled to vote on any amendment to this Certificate (or on any amendment to
a certificate of designations of any series of Undesignated Preferred Stock)
that alters or changes the powers, preferences, rights or other terms of one or
more outstanding series or class of Preferred Stock if the holders of such
affected series or class are entitled to vote, either separately or together
with the holders of one or more other such series or classes, on such amendment
pursuant to this Certificate (or pursuant to a certificate of designations of
any series of Undesignated Preferred Stock) or pursuant to the DGCL;

                                       2
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               (b)  dividends may be declared and paid or set apart for payment
upon the Common Stock out of any assets or funds of the Corporation legally
available for the payment of dividends, but only when and as declared by the
Board of Directors or any authorized committee thereof; and

               (c)  upon the voluntary or involuntary liquidation, dissolution
or winding up of the Corporation, the net assets of the Corporation shall be
distributed pro rata to the holders of the Common Stock.

                         B.  SERIES Z PREFERRED STOCK
                             ------------------------

     1.   Designation and Amount. The total number of shares of Series Z
          ----------------------
Preferred Stock which the Corporation shall have authority to issue is One
Million (1,000,000) shares.

     2.   Dividends and Distributions.
          ---------------------------

          (a)  (i)  Subject to the rights of the holders of any shares of any
series of Undesignated Preferred Stock (or any similar stock) ranking prior and
superior to the Series Z Preferred Stock with respect to dividends, the holders
of shares of Series Z Preferred Stock, in preference to the holders of shares of
Common Stock and of any other junior stock, shall be entitled to receive, when,
as and if declared by the Board of Directors out of funds legally available for
the purpose, quarterly dividends payable in cash on the first day of March,
June, September and December in each year (each such date being referred to
herein as a "Quarterly Dividend Payment Date"), commencing on the first
Quarterly Dividend Payment Date after the first issuance of a share or fraction
of a share of Series Z Preferred Stock, in an amount per share (rounded to the
nearest cent) equal to the greater of (a) $1.00 or (b) subject to the provisions
for adjustment hereinafter set forth, 1,000 times the aggregate per share amount
of all cash dividends, and 1,000 times the aggregate per share amount (payable
in kind) of all non-cash dividends or other distributions other than a dividend
payable in shares of Common Stock or a subdivision of the outstanding shares of
Common Stock (by reclassification or otherwise), declared on the Common Stock
since the immediately preceding Quarterly Dividend Payment Date, or, with
respect to the first Quarterly Dividend Payment Date, since the first issuance
of any share or fraction of a share of Series Z Preferred Stock.  The multiple
of cash and non-cash dividends declared on the Common Stock to which holders of
the Series Z Preferred Stock are entitled, which shall be 1,000 initially but
which shall be adjusted from time to time as hereinafter provided, is
hereinafter referred to as the "Dividend Multiple."  In the event the
Corporation shall at any time after February 9, 2000 (the "Rights Declaration
Date") (i) declare or pay any dividend on Common Stock payable in shares of
Common Stock, or (ii) effect a subdivision or combination or consolidation of
the outstanding shares of Common Stock (by reclassification or otherwise than by
payment of a dividend in shares of Common Stock) into a greater or lesser number
of shares of Common Stock, then in each such case the Dividend Multiple
thereafter applicable to the determination of the amount of dividends which
holders of shares of Series Z Preferred Stock shall be entitled to receive shall
be the Dividend Multiple applicable immediately prior to such event multiplied
by a fraction,

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the numerator of which is the number of shares of Common Stock outstanding
immediately after such event and the denominator of which is the number of
shares of Common Stock that were outstanding immediately prior to such event.

               (ii) Notwithstanding anything else contained in this paragraph
(a), the Corporation shall, out of funds legally available for that purpose,
declare a dividend or distribution on the Series Z Preferred Stock as provided
in this paragraph (a) immediately after it declares a dividend or distribution
on the Common Stock (other than a dividend payable in shares of Common Stock);
provided that, in the event no dividend or distribution shall have been declared
on the Common Stock during the period between any Quarterly Dividend Payment
Date and the next subsequent Quarterly Dividend Payment Date, a dividend of
$1.00 per share on the Series Z Preferred Stock shall nevertheless be payable on
such subsequent Quarterly Dividend Payment Date.

          (b)  Dividends shall begin to accrue and be cumulative on outstanding
shares of Series Z Preferred Stock from the Quarterly Dividend Payment Date next
preceding the date of issue of such shares of Series Z Preferred Stock, unless
the date of issue of such shares is prior to the record date for the first
Quarterly Dividend Payment Date, in which case dividends on such shares shall
begin to accrue from the date of issue of such shares, or unless the date of
issue is a Quarterly Dividend Payment Date or is a date after the record date
for the determination of holders of shares of Series Z Preferred Stock entitled
to receive a quarterly dividend and before such Quarterly Dividend Payment Date,
in either of which events such dividends shall begin to accrue and be cumulative
from such Quarterly Dividend Payment Date.  Accrued but unpaid dividends shall
not bear interest.  Dividends paid on the shares of Series Z Preferred Stock in
an amount less than the total amount of such dividends at the time accrued and
payable on such shares shall be allocated pro rata on a share-by-share basis
among all such shares at the time outstanding.  The Board of Directors may fix
in accordance with applicable law a record date for the determination of holders
of shares of Series Z Preferred Stock entitled to receive payment of a dividend
or distribution declared thereon, which record date shall be not more than such
number of days prior to the date fixed for the payment thereof as may be allowed
by applicable law.

     3.   Voting Rights.  In addition to any other voting rights required by
          -------------
law, the holders of shares of Series Z Preferred Stock shall have the following
voting rights:

          (a)  Subject to the provision for adjustment hereinafter set forth,
each share of Series Z Preferred Stock shall entitle the holder thereof to 1,000
votes on all matters submitted to a vote of the stockholders of the Corporation.
The number of votes which a holder of a share of Series Z Preferred Stock is
entitled to cast, which shall initially be 1,000 but which may be adjusted from
time to time as hereinafter provided, is hereinafter referred to as the "Vote
Multiple."  In the event the Corporation shall at any time after the Rights
Declaration Date (i) declare or pay any dividend on Common Stock payable in
shares of Common Stock, or (ii) effect a subdivision or combination or
consolidation of the outstanding shares of Common Stock (by reclassification or
otherwise than by payment of a dividend in

                                       4
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shares of Common Stock) into a greater or lesser number of shares of Common
Stock, then in each such case the Vote Multiple thereafter applicable to the
determination of the number of votes per share to which holders of shares of
Series Z Preferred Stock shall be entitled shall be the Vote Multiple
immediately prior to such event multiplied by a fraction, the numerator of which
is the number of shares of Common Stock outstanding immediately after such event
and the denominator of which is the number of shares of Common Stock that were
outstanding immediately prior to such event.

          (b)  Except as otherwise provided herein or by law, the holders of
shares of Series Z Preferred Stock and the holders of shares of Common Stock and
the holders of shares of any other capital stock of this Corporation having
general voting rights, shall vote together as one class on all matters submitted
to a vote of stockholders of the Corporation.

          (c)  Except as otherwise required by applicable law or as set forth
herein, holders of Series Z Preferred Stock shall have no special voting rights
and their consent shall not be required (except to the extent they are entitled
to vote with holders of Common Stock as set forth herein) for taking any
corporate action.

     4.   Certain Restrictions.
          --------------------

          (a)  Whenever dividends or distributions payable on the Series Z
Preferred Stock as provided in Section B.2 are in arrears, thereafter and until
all accrued and unpaid dividends and distributions, whether or not declared, on
shares of Series Z Preferred Stock outstanding shall have been paid in full, the
Corporation shall not:

               (i)    declare or pay dividends on, make any other distributions
                      on, or redeem or purchase or otherwise acquire for
                      consideration any shares of stock ranking junior (either
                      as to dividends or upon liquidation, dissolution or
                      winding up) to the Series Z Preferred Stock;

               (ii)   declare or pay dividends on or make any other
                      distributions on any shares of stock ranking on a parity
                      (either as to dividends or upon liquidation, dissolution
                      or winding up) with the Series Z Preferred Stock, except
                      dividends paid ratably on the Series Z Preferred Stock and
                      all such parity stock on which dividends are payable or in
                      arrears in proportion to the total amounts to which the
                      holders of all such shares are then entitled;

               (iii)  except as permitted in subsection B.4(a)(iv) below,
                      redeem, purchase or otherwise acquire for consideration
                      shares of any stock ranking on a parity (either as to
                      dividends or upon liquidation, dissolution or winding up)
                      with the Series Z Preferred Stock, provided that the
                      Corporation may at any time

                                       5
<PAGE>

                      redeem, purchase or otherwise acquire shares of any such
                      parity stock in exchange for shares of any stock of the
                      Corporation ranking junior (either as to dividends or upon
                      dissolution, liquidation or winding up) to the Series Z
                      Preferred Stock; or

               (iv)   purchase or otherwise acquire for consideration any shares
                      of Series Z Preferred Stock, or any shares of any stock
                      ranking on a parity (either as to dividends or upon
                      liquidation, dissolution or winding up) with the Series Z
                      Preferred Stock, except in accordance with a purchase
                      offer made in writing or by publication (as determined by
                      the Board of Directors) to all holders of such shares upon
                      such terms as the Board of Directors, after consideration
                      of the respective annual dividend rates and other relative
                      rights and preferences of the respective series and
                      classes, shall determine in good faith will result in fair
                      and equitable treatment among the respective series or
                      classes.

          (b)  The Corporation shall not permit any subsidiary of the
Corporation to purchase or otherwise acquire for consideration any shares of
stock of the Corporation unless the Corporation could, under subsection (a) of
this Section B.4, purchase or otherwise acquire such shares at such time and in
such manner.

     5.   Reacquired Shares.  Any shares of Series Z Preferred Stock purchased
          -----------------
or otherwise acquired by the Corporation in any manner whatsoever shall be
retired and canceled promptly after the acquisition thereof.

     6.   Liquidation, Dissolution or Winding Up.  Upon any liquidation
          --------------------------------------
(voluntary or otherwise), dissolution or winding up of the Corporation, no
distribution shall be made (x) to the holders of shares of stock ranking junior
(either as to dividends or upon liquidation, dissolution or winding up) to the
Series Z Preferred Stock unless, prior thereto, the holders of shares of Series
Z Preferred Stock shall have received an amount equal to accrued and unpaid
dividends and distributions thereon, whether or not declared, to the date of
such payment, plus an amount equal to the greater of (1) $1,000.00 per share or
(2) an aggregate amount per share, subject to the provision for adjustment
hereinafter set forth, equal to 1,000 times the aggregate amount to be
distributed per share to holders of Common Stock, or (y) to the holders of stock
ranking on a parity (either as to dividends or upon liquidation, dissolution or
winding up) with the Series Z Preferred Stock, except distributions made ratably
on the Series Z Preferred Stock and all other such parity stock in proportion to
the total amounts to which the holders of all such shares are entitled upon such
liquidation, dissolution or winding up.  In the event the Corporation shall at
any time after the Rights Declaration Date (i) declare or pay any dividend on
Common Stock payable in shares of Common Stock, or (ii) effect a subdivision or
combination or consolidation of the outstanding shares of Common Stock (by
reclassification or otherwise than by payment of a dividend in shares of Common
Stock) into a greater or lesser number of shares of Common Stock, then in each
such case the aggregate amount per

                                       6
<PAGE>

share to which holders of shares of Series Z Preferred Stock were entitled
immediately prior to such event under clause (x) of the preceding sentence shall
be adjusted by multiplying such amount by a fraction, the numerator of which is
the number of shares of Common Stock outstanding immediately after such event
and the denominator of which is the number of shares of Common Stock that were
outstanding immediately prior to such event.

     Neither the consolidation of nor merging of the Corporation with or into
any other corporation or corporations, nor the sale or other transfer of all or
substantially all of the assets of the Corporation, shall be deemed to be a
liquidation, dissolution or winding up of the Corporation within the meaning of
this Section B.6.

     7.   Consolidation, Merger, etc.  In case the Corporation shall enter into
          --------------------------
any consolidation, merger, combination or other transaction in which the shares
of Common Stock are exchanged for or changed into other stock or securities,
cash and/or any other property, then in any such case the shares of Series Z
Preferred Stock shall at the same time be similarly exchanged or changed in an
amount per share (subject to the provision for adjustment hereinafter set forth)
equal to 1,000 times the aggregate amount of stock, securities, cash and/or any
other property (payable in kind), as the case may be, into which or for which
each share of Common Stock is changed or exchanged, plus accrued and unpaid
dividends, if any, payable with respect to the Series Z Preferred Stock.  In the
event the Corporation shall at any time after the Rights Declaration Date (i)
declare or pay any dividend on Common Stock payable in shares of Common Stock,
or (ii) effect a subdivision or combination or consolidation of the outstanding
shares of Common Stock (by reclassification or otherwise than by payment of a
dividend in shares of Common Stock) into a greater or lesser number of shares of
Common Stock, then in each such case the amount set forth in the preceding
sentence with respect to the exchange or change of shares of Series Z Preferred
Stock shall be adjusted by multiplying such amount by a fraction, the numerator
of which is the number of shares of Common Stock outstanding immediately after
such event and the denominator of which is the number of shares of Common Stock
that were outstanding immediately prior to such event.

     8.   Redemption.  The shares of Series Z Preferred Stock shall not be
          ----------
redeemable; provided, however, that the foregoing shall not limit the ability of
the Corporation to purchase or otherwise deal in such shares to the extent
otherwise permitted hereby and by law.

     9.   Ranking.  Unless otherwise expressly provided in this Certificate or a
          -------
certificate of designations relating to any other series of Undesignated
Preferred Stock, the Series Z Preferred Stock shall rank junior to every other
series of Undesignated Preferred Stock hereafter authorized, as to the payment
of dividends and the distribution of assets on liquidation, dissolution or
winding up and shall rank senior to the Common Stock.

     10.  Amendment.  This Certificate shall not be amended in any manner which
          ---------
would materially alter or change the powers, preferences or special rights of
the Series Z Preferred Stock so as to affect them adversely without the
affirmative vote of the holders of two-thirds or more of the outstanding shares
of Series Z Preferred Stock, voting separately as a class.

                                       7
<PAGE>

     11.  Fractional Shares.  Series Z Preferred Stock may be issued in whole
          -----------------
shares or in any fraction of a share that is one one-thousandth (1/1,000th) of a
share or any integral multiple of such fraction, which shall entitle the holder,
in proportion to such holder's fractional shares, to exercise voting rights,
receive dividends, participate in distributions and to have the benefit of all
other rights of holders of Series Z Preferred Stock.  In lieu of fractional
shares, the Corporation may elect to make a cash payment as provided in the
Shareholder Rights Agreement, between the Corporation and State Street Bank &
Trust Company, for fractions of a share other than one one-thousandth
(1/1,000th) of a share or any integral multiple thereof.

                       C.  UNDESIGNATED PREFERRED STOCK
                           ----------------------------

     The Board of Directors or any authorized committee thereof is expressly
authorized, to the fullest extent permitted by law, to provide for the issuance
of the shares of Undesignated Preferred Stock in one or more series of such
stock, and by filing a certificate pursuant to applicable law of the State of
Delaware, to establish or change from time to time the number of shares of each
such series, and to fix the designations, powers, including voting powers, full
or limited, or no voting powers, preferences and the relative, participating,
optional or other special rights of the shares of each series and any
qualifications, limitations and restrictions thereof.

                                   ARTICLE V

                               STOCKHOLDER ACTION
                               ------------------

     1.   Action without Meeting.  Except as otherwise provided herein, any
          ----------------------
action required or permitted to be taken by the stockholders of the Corporation
at any annual or special meeting of stockholders of the Corporation must be
effected at a duly called annual or special meeting of stockholders and may not
be taken or effected by a written consent of stockholders in lieu thereof.

     2.   Special Meetings.  Except as otherwise required by statute and subject
          ----------------
to the rights, if any, of the holders of any series or class of Preferred Stock,
special meetings of the stockholders of the Corporation may be called only by
the Board of Directors acting pursuant to a resolution approved by the
affirmative vote of a majority of the Directors then in office.  Only those
matters set forth in the notice of the special meeting may be considered or
acted upon at a special meeting of stockholders of the Corporation.

                                       8
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                                  ARTICLE VI

                                   DIRECTORS
                                   ---------

     1.   General.  The business and affairs of the Corporation shall be managed
          -------
by or under the direction of the Board of Directors except as otherwise provided
herein or required by law.

     2.   Election of Directors.  Election of Directors need not be by written
          ---------------------
ballot unless the By-laws of the Corporation (the "By-laws") shall so provide.

     3.   Number of Directors; Term of Office.  The number of Directors of the
          -----------------------------------
Corporation shall be fixed solely and exclusively by resolution duly adopted
from time to time by the Board of Directors.  The Directors, other than those
who may be elected by the holders of any series or class of Preferred Stock,
shall be classified, with respect to the term for which they severally hold
office, into three classes, as nearly equal in number as reasonably possible.
The initial Class I Directors of the Corporation shall be Ward C. Bourdeaux,
Jr., William P. Egan and Jeffrey H. Schutz; the initial Class II Directors of
the Corporation shall be Laurence S. Grafstein, Randall A. Hack and P. Eric
Yopes; and the initial Class III Directors of the Corporation shall be R.
Stanley Allen and John C. Halsted. The initial Class I Directors shall serve for
a term expiring at the annual meeting of stockholders to be held in 2000, the
initial Class II Directors shall serve for a term expiring at the annual meeting
of stockholders to be held in 2001, and the initial Class III Directors shall
serve for a term expiring at the annual meeting of stockholders to be held in
2002.  At each annual meeting of stockholders, Directors elected to succeed
those Directors whose terms expire shall be elected for a term of office to
expire at the third succeeding annual meeting of stockholders after their
election.  Notwithstanding the foregoing, the Directors elected to each class
shall hold office until their successors are duly elected and qualified or until
their earlier resignation or removal.

     Notwithstanding the foregoing, whenever, pursuant to the provisions of
Article IV of this Certificate, the holders of any one or more series or classes
of Preferred Stock shall have the right, voting separately as a series or class
or together with holders of other such series or classes, to elect Directors at
an annual or special meeting of stockholders, the election, term of office,
filling of vacancies and other features of such directorships shall be governed
by the terms of this Certificate and any certificate of designations applicable
thereto.

     4.   Vacancies.  Subject to the rights, if any, of the holders of any
          ---------
series or class of Preferred Stock to elect Directors and to fill vacancies in
the Board of Directors relating thereto, any and all vacancies in the Board of
Directors, however occurring, including, without limitation, by reason of an
increase in size of the Board of Directors, or the death, resignation,
disqualification or removal of a Director, shall be filled solely and
exclusively by the affirmative vote of a majority of the remaining Directors
then in office, even if less than a quorum of the Board of Directors, and not by
the stockholders.  Any Director appointed in accordance with the preceding
sentence shall hold office for the remainder of the full term of

                                       9
<PAGE>

the class of Directors in which the new directorship was created or the vacancy
occurred and until such Director's successor shall have been duly elected and
qualified or until his or her earlier resignation or removal. Subject to the
rights, if any, of the holders of any series or class of Preferred Stock to
elect Directors, when the number of Directors is increased or decreased, the
Board of Directors shall, subject to Article VI.3 hereof, determine the class or
classes to which the increased or decreased number of Directors shall be
apportioned; provided, however, that no decrease in the number of Directors
             --------  -------
shall shorten the term of any incumbent Director. In the event of a vacancy in
the Board of Directors, the remaining Directors, except as otherwise provided by
law, shall exercise the powers of the full Board of Directors until the vacancy
is filled.

     5.   Removal.  Subject to the rights, if any, of any series or class of
          -------
Preferred Stock to elect Directors and to remove any Director whom the holders
of any such stock have the right to elect, any Director (including persons
elected by Directors to fill vacancies in the Board of Directors) may be removed
from office (i) only with cause and (ii) only by the affirmative vote of the
holders of 75% or more of the shares then entitled to vote at an election of
Directors.  At least forty-five (45) days prior to any meeting of stockholders
at which it is proposed that any Director be removed from office, written notice
of such proposed removal and the alleged grounds thereof shall be sent to the
Director whose removal will be considered at the meeting.

                                  ARTICLE VII

                            LIMITATION OF LIABILITY
                            -----------------------

     A Director of the Corporation shall not be personally liable to the
Corporation or its stockholders for monetary damages for breach of fiduciary
duty as a Director, except for liability (a) for any breach of the Director's
duty of loyalty to the Corporation or its stockholders, (b) for acts or
omissions not in good faith or which involve intentional misconduct or a knowing
violation of law, (c) under Section 174 of the DGCL or (d) for any transaction
from which the Director derived an improper personal benefit.  If the DGCL is
amended after the effective date of this Certificate 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 DGCL, as so amended.

     Any repeal or modification of this Article VII by either of (i) the
stockholders of the Corporation or (ii) an amendment to the DGCL, shall not
adversely affect any right or protection existing at the time of such repeal or
modification with respect to any acts or omissions occurring before such repeal
or modification of a person serving as a Director at the time of such repeal or
modification.

                                       10
<PAGE>

                                 ARTICLE VIII

                             AMENDMENT OF BY-LAWS
                             --------------------

     1.   Amendment by Directors.  Except as otherwise provided by law, the By-
          ----------------------
laws of the Corporation may be amended or repealed by the Board of Directors by
the affirmative vote of a majority of the Directors then in office.

     2.   Amendment by Stockholders.  The By-laws of the Corporation may be
          -------------------------
amended or repealed at any annual meeting of stockholders, or special meeting of
stockholders called for such purpose as provided in the By-laws, by the
affirmative vote of at least 75% of the shares present in person or represented
by proxy at such meeting and entitled to vote on such amendment or repeal,
voting together as a single class; provided, however, that if the Board of
                                   --------  -------
Directors recommends that stockholders approve such amendment or repeal at such
meeting of stockholders, such amendment or repeal shall only require the
affirmative vote of the majority of the shares present in person or represented
by proxy at such meeting and entitled to vote on such amendment or repeal,
voting together as a single class.

                                  ARTICLE IX

                   AMENDMENT OF CERTIFICATE OF INCORPORATION
                   -----------------------------------------

     The Corporation reserves the right to amend or repeal this Certificate in
the manner now or hereafter prescribed by statute and this Certificate, and all
rights conferred upon stockholders herein are granted subject to this
reservation.  Whenever any vote of the holders of voting stock is required to
amend or repeal any provision of this Certificate, and in addition to any other
vote of holders of voting stock that is required by this Certificate or by law,
such amendment or repeal shall require the affirmative vote of the majority of
the outstanding shares entitled to vote on such amendment or repeal, and the
affirmative vote of the majority of the outstanding shares of each class
entitled to vote thereon as a class, at a duly constituted meeting of
stockholders called expressly for such purpose; provided, however, that the
                                                --------  -------
affirmative vote of not less than 75% of the outstanding shares entitled to vote
on such amendment or repeal, and the affirmative vote of not less than 75% of
the outstanding shares of each class entitled to vote thereon as a class, shall
be required to amend or repeal any provision of Article V, Article VI, Article
VII, Article IX or Article X of this Certificate.

                                   ARTICLE X

                             BUSINESS COMBINATIONS
                             ---------------------

     The Corporation elects to be governed by the provisions of Section 203 of
the DGCL.


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                                       11
<PAGE>

     IN WITNESS WHEREOF, the Corporation has caused this Second Amended and
Restated Certificate of Incorporation to be signed by R. Stanley Allen, its
Chief Executive Officer, this 15th day of February, 2000, which signature
constitutes the affirmation or acknowledgment of such officer, under penalties
of perjury, that this instrument is the act and deed of the Corporation, and
that the facts stated therein are true.


                                    CYPRESS COMMUNICATIONS, INC.


                                    By: /s/ R. Stanley Allen
                                       ------------------------------
                                       R. Stanley Allen
                                       Chief Executive Officer