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                                                                  Exhibit 10.4

                           CERTIFICATE OF CORRECTION
                                      OF
                         CERTIFICATE OF DESIGNATION OF
              6% SERIES E CUMULATIVE CONVERTIBLE PREFERRED STOCK
                                      OF
                    AMERICAN TELESOURCE INTERNATIONAL, INC.


     American TeleSource International, Inc., a corporation organized and
existing under and by virtue of the General Corporation Law of the State of
Delaware,

     DOES HEREBY CERTIFY:

     1.  The name of the corporation is American TeleSource International, Inc.

     2.  A Certificate of Designation of the 6% Series E Cumulative Convertible
Preferred Stock of American TeleSource International, Inc. (the "Certificate of
Designation") was filed with the Secretary of State of Delaware on October 10,
2000 and was corrected by means of a Certificate of Correction filed with the
Secretary of State of Delaware on October 11, 2000. The Certificate of
Designation requires additional correction as permitted by Section 103 of the
General Corporation Law of the State of Delaware.

     3.  The reference to "$1.3125" in the tenth line of the first sentence of
Article V.C of the Certificate of Designation should be replaced with " 75% of
the Issuance Price (as defined below)".

     4.  The first sentence of Article VI.B(i) of the Certificate of Designation
is hereby corrected to read in its entirety as follows:

             (i)  Calculation of Conversion Price.  Subject to subparagraph (ii)
                  -------------------------------
         below, the "Conversion Price" shall be the lesser of the Market Price
         (as defined herein) and the Fixed Conversion Price (as defined herein),
         subject to adjustments pursuant to the provisions of Article VI.C
         below; provided, however, that the Conversion Price shall not be less
         than 75% of the Issuance Price (as defined below)(subject to equitable
         adjustments from time to time for stock splits, stock dividends,
         combinations, capital reorganizations and similar events relating to
         the Common Stock occurring after the Issue Date) (the "Floor Price")
         unless at any time after the Issue Date the Closing Bid Price of the
         Common Stock is less than Floor Price for any ten (10) Trading Days
         during any twenty (20) consecutive Trading Day period (a "Floor Price
         Termination Event"). Upon the occurrence of a Floor Price



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         Termination Event, the Floor Price will permanently be eliminated and
         the limitations on the Conversion Price pursuant to the proviso in the
         preceding sentence shall terminate. "Market Price" shall mean the
         average of the five (5) lowest Closing Bid Prices (the "Market Price
         Days"), during the ten (10) consecutive Trading Day period ending one
         (1) Trading Day prior to the date the Notice of Conversion (as defined
         in Article VI.D) is sent by a holder to the Corporation via facsimile
         (the "Pricing Period"). The Market Price Days shall be designated by
         the converting holder (from among the days comprising the Pricing
         Period) in the Notice of Conversion. "Fixed Conversion Price" shall
         mean 120% of the Issuance Price (as defined below); provided, however,
                                                             --------  -------
         that if the average of the Closing Bid Prices for the lowest five (5)
         consecutive Trading Days during the twenty (20) consecutive Trading Day
         period ending (the "Reset Price") on the Reset Date is less than the
         Fixed Conversion Price, at all times after the Reset Date the Fixed
         Conversion Price shall equal the Reset Price; provided further,
                                                       -------- -------
         however, that if the Corporation issues or sells any Equity Securities
         -------
         (as defined in the Securities Purchase Agreement) pursuant to the
         Equity Line (as defined in the Securities Purchase Agreement), "Fixed
         Conversion Price" shall mean, for all conversions following the closing
         date for such issuance or sale, the lesser of (A) the Fixed Conversion
         Price otherwise in effect on such closing date, (B) the average Closing
         Bid Price for the Common Stock during the ten (10) consecutive Trading
         Day period immediately preceding (but not including) such closing date
         and (C) the purchase price per share of the Common Stock being issued
         pursuant to the Equity Line (an "Equity Line Adjustment"). The Fixed
         Conversion Price shall be subject to an Equity Line Adjustment each
         time that the Corporation issues or sells Equity Securities pursuant to
         the Equity Line. The "Issuance Price" shall mean the lowest Closing Bid
         Price during the three Trading Day period beginning on October 11,
         2000, and ending on October 13, 2000. "Closing Bid Price" means, for
         any security as of any date, the closing bid price on the AMEX as
         reported by Bloomberg or, if the AMEX is not the principal trading
         market for such security, the closing bid price of such security on the
         principal securities exchange or trading market where such security is
         listed or traded as reported by Bloomberg, or if the foregoing do not
         apply, the closing bid price of such security in the over-the-counter
         market on the electronic bulletin board for such security as reported
         by Bloomberg, or, if no closing bid price of such security is available
         in the over-the-counter market on the electronic bulletin board for
         such security or in any of the foregoing manners, the average of the
         bid prices of any



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         market makers for such security that are listed in the "pink sheets" by
         the National Quotation Bureau, Inc. If the Closing Bid Price cannot be
         calculated for such security on such date in the manner provided above,
         the Closing Bid Price shall be the fair market value as mutually
         determined by the Corporation and the holders of a majority in interest
         of shares of Series E Preferred Stock being converted for which the
         calculation of the Closing Bid Price is required in order to determine
         the Conversion Price of such Series E Preferred Stock. "Trading Day"
         shall mean any day on which the Common Stock is traded for any period
         on the AMEX, or on the principal securities exchange or other
         securities market on which the Common Stock is then being traded.

     5.  The phrase "175% of the Conversion Price" in the twenty-eighth line of
the first sentence of Article VII of the Certificate of Designation should be
replaced with "175% of the Fixed Conversion Price".

               [REMAINDER OF THIS PAGE INTENTIONALLY LEFT BLANK]



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     IN WITNESS WHEREOF, this Certificate of Correction is executed on behalf of
the Corporation this 12th Day of October, 2000.

                                         AMERICAN TELESOURCE INTERNATIONAL, INC.



                                         By: /c/ H. Douglas Saathoff
                                             -----------------------
                                         Name:  H. Douglas Saathoff
                                         Title:  Senior Executive Vice President


                                         By:/c/ Raymond G. Romero
                                            -----------------------
                                         Name:  Raymond G. Romero
                                         Title:  Secretary