A digital mobile communication system comprises a mobile station (MS) with a facsimile adapter (2), a first telefax terminal (1) connected to the adapter, a mobile network (BSS, MSC), an interworking unit (32) with a second facsimile adapter (33). A high-speedtransparent rate-adapted facsimile connection is set up between the telefax terminals. The number of parallel traffic channels (ch0-chn) allocated to the high-speed data connection is such that the maximum data rate of the data connection is higher than the allowed maximum data rate of the telefax terminals (1, 10). The telefax terminals may negotiate the facsimile data rate. The second facsimile adapter (33) monitors the negociation and selects, on the basis of the negociated facsimile data rate, the most effective channel coding available for the data connection.