<Page>

                                                                     EXHIBIT 3.4

                          CERTIFICATE OF INCORPORATION
                                       OF
                             IESI TX GP CORPORATION

     I, the undersigned natural person acting as an incorporator of a
corporation (the "Company") under the General Corporation Law of the State of
Delaware (the "Delaware General Corporation Law"), hereby adopt the following
Certificate of Incorporation (the "Certificate") for the Company:

                                   ARTICLE ONE

     The name of the Company is IESI TX GP Corporation.

                                   ARTICLE TWO

     The registered office of the Company in the State of Delaware is
Corporation Service Company, 1013 Centre Road, Wilmington, Delaware 19805. The
name of its Registered Agent at the above address is Corporation Service
Company.

                                  ARTICLE THREE

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

                                  ARTICLE FOUR

     The total number of shares of capital stock that the Company has authority
to issue is 1,000 shares, which will be designated Common stock, par value $.01
per share.

                                  ARTICLE FIVE

     The name and mailing address of the Incorporator are as follows:

            NAME                        ADDRESS

            Theresa H. Lewis            201 Main Street, Suite 2500
                                        Fort Worth, Texas 76102

                                   ARTICLE SIX

     Unless, and except to the extent that, the By-Laws of the Company (the
"By-Laws") so require, the election of directors need not be by written ballot.

                                  ARTICLE SEVEN

     The board of directors of the Company (the "Board of Directors") may from
time to time adapt, amend or repeal the By-Laws, subject to the power of the
stockholders to adopt any By-Laws

<Page>

or to amend or repeal any By-Laws adopted, amended or repealed by the Board of
Directors.

                                  ARTICLE EIGHT

     To the fullest event that the Delaware General Corporation Law as it exists
on the date hereof or as it may hereafter be amended permits the limitation or
elimination of the liability of directors, no director will be liable to the
Company or its stockholders for monetary damage for breach of fiduciary duty as
a director. Any repeal or amendment of this Article will not adversely affect
any limitation on the personal liability or alleged liability of a director
arising from an act or omission of that director occurring prior to the time of
such repeal or amendment.

     THE UNDERSIGNED INCORPORATOR, for the purposes of forming the corporation,
does make and file this Certificate of Incorporation, hereby declaring and
certifying that the facts herein stated are true and accordingly has set her
hand on June 10, 1999.

                                       /s/ Theresa B. Lewis
                                       ---------------------------------
                                       THERESA B. LEWIS

                                       -2-