Variable bit rate (VBR) transmission is widely regarded as the best solution for the transport of compressed image and video data, both in terms of network utilization and quality of data decoded at the receiver. However, significant problems remain unsolved to make this a viable approach. One of these problems is that of efficiently matching characteristics of the VBR source to those of the channel, in order to maximize end-to-end system performance. In this work, we propose a model for the channel based on which the source can make optimal decisions regarding bit allocation and rate control. This model consists of N queues, for each of which the source negotiates with the network statistical performance guarantees, consisting of allowable average transmission and packet loss rates. Based on such a channel description, the source determines how to allocate packets to each queue, to minimize the expected distortion of the images reconstructed at the receiver. A provably optimal algorithm for computing such bit allocations is the core of this work. Simulation results are presented.