In UMTS technology, Coded Composite Transport Channels (CCTrCh-s) are used to carry multiple Transport Channels (TrCh-s) in parallel on (usually) one physical layer connection. Rate Matching Attributes (RMA-s) are used to share the CCTrCh resources among the transport channels. We consider I transport channels on the downlink of a UMTS network, with RMA values RMA1, RMA2,…, RMAI. The QoS experienced by the multiplexed connections depends on the RMA values used. We derive analytical expressions for the Bit Error Probabilities (BER-s) seen by each uncoded TrCh in the multiplex when transmitted over an AWGN and a multipath channel. Simulations indicate that the expressions are very accurate. Next, we derive analytical expressions for bounds on the per-channel bit error probabilities seen when convolutional coding is employed by each channel and the multiplex is transmitted over an AWGN and a multipath channel, respectively. The derivation of these analytical expressions is the main contribution of this paper. Further, we use the expressions to obtain simple procedures that provide the RMA values required to achieve a target set of BER-s for a specified signal-to-noise ratio. The results of this paper indicate how differentiated QoS may be provided while maintaining high spectral efficiency.