<PAGE>
                                                                     EXHIBIT 3.3

 
                             ARTICLES OF AMENDMENT
                                     TO THE
                           ARTICLES OF INCORPORATION



     Pursuant to the provisions of the Colorado Business Corporation Act, the
undersigned Corporation adopts the following Articles of Amendment to its
Articles of Incorporation:

     FIRST:    The name of the Corporation is JONES INTERCABLE, INC.

     SECOND:   The following amendments were adopted by the shareholders of the
               Corporation on September 17, 1996, and the number of votes cast
               for the amendments by each voting group entitled to vote
               separately on the amendments was sufficient for approval by that
               voting group:

               Provision NINTH of the Articles of Incorporation of the
     Corporation shall be amended by striking out and eliminating the existing
     text thereof in its entirety and substituting the following in its place:

          "NINTH:  The Corporation shall indemnify, to the fullest extent
     permitted by applicable law in effect from time to time, any person, and
     the estate and personal representative of any such person, against all
     liability and expense (including attorneys' fees) incurred by reason of the
     fact that such person is or was a director or officer of the Corporation
     or, while serving as a director or officer of the Corporation, such person
     is or was serving at the Corporation's request as a director, officer,
     partner, trustee, employee, fiduciary or agent of, or in any similar
     managerial or fiduciary position of, another domestic or foreign
     corporation or other individual or entity or of an employee benefit plan.
     The Corporation shall also indemnify any person who is serving or who has
     served the Corporation as a director, officer, employee, fiduciary or
     agent, and such person's estate and personal representative, to the extent
     and in the manner provided in any by-law, resolution of the shareholders or
     directors, contract or otherwise, so long as such provision is legally
     permissible."

     ; and
<PAGE>
 
          An ELEVENTH provision shall be added to the Articles of Incorporation
     of the Corporation as follows:

          "ELEVENTH:  No director of the Corporation shall have any personal
     liability for monetary damages to the corporation or its shareholders for
     breach of his or her fiduciary duty as a director, except that this
     provision shall not eliminate or limit the personal liability of a director
     to the Corporation or its shareholders for monetary damages for:  (i) any
     breach of the director's duty of loyalty to the Corporation or its
     shareholders; (ii) acts or omissions not in good faith or which involve
     intentional misconduct or a knowing violation of law; (iii) acts specified
     in Section 7-108-403 of the Colorado Business Corporation Act; or (iv) any
     transaction from which the director directly or indirectly derives an
     improper personal benefit.  Nothing contained herein will be construed to
     eliminate or diminish the defenses ordinarily available to a director or to
     deprive any director of any right he or she may have for contribution from
     any other director or other person.  If the Colorado Business Corporation
     Act hereafter is amended to eliminate or limit further the liability of a
     director, then, in addition to the elimination and limitation of liability
     provided by the preceding sentences, the liability of each director shall
     be eliminated or limited to the fullest extent permitted by the Colorado
     Business Corporation Act as so amended.  Any repeal or modification of this
     Article shall not adversely affect any right or protection of a director of
     the Corporation under this Article as in effect immediately prior to such
     repeal or modification with respect to any liability that would have
     accrued, but for this Article, prior to such repeal or modification."

     THIRD:    The manner, if not set forth in such amendment, in which any
               exchange, reclassification, or cancellation of issued shares
               provided for in the amendment shall be effected, is as follows:

               No change.

                              JONES INTERCABLE, INC.,
                              a Colorado corporation


                              By:   /s/ Elizabeth M. Steele
                                    -----------------------
                                    Elizabeth M. Steele
                                    Vice President

                                       2