A transmission arrangement is disclosed which facilitates compression of modem modulated facsimile signals for transmission on digital facilities. The presence of a facsimile call is detected and facsimile control messages are obtained by demodulating and interpreting the facsimile call control protocol (111). A controller (114) is responsive to the obtained control messages for controlling a voiceband encoder (110) to encode the control portion of the facsimile call and for controlling a so-called facsimile page demodulator (112) to demodulate any facsimile page portions of the facsimile call to obtain a baseband digital bit stream. The encoded control portion of the facsimile call and the baseband digital bit stream representative of the demodulated, i.e. compressed, facsimile page portion of the facsimile call are transmitted along with control information (as side information) to a receiver (103). At the receiver, a replica of the original modem modulated facsimile signal is reconstructed in response to the control information and by decoding the control portion of the facsimile call and by remodulating the digital bit stream representative of the facsimile page portion of the facsimile call.