Consider the problem of transmitting multiple video streams to fulfill a constant bandwidth constraint. The available bit budget needs to be distributed across the sequences in order to meet some optimality criteria. For example, one might want to minimize the average distortion or, alternatively, minimize the distortion variance, in order to keep almost constant quality among the encoded sequences. By working in the rho-domain, we propose a low-delay rate allocation scheme that, at each time instant, provides a closed form solution for either the aforementioned problems. We show that minimizing the distortion variance instead of the average distortion leads, for each of the multiplexed sequences, to a coding penalty less than 0.5 dB, in terms of average PSNR. In addition, our analysis provides an explicit relationship between model parameters and this loss. In order to smooth the distortion also along time, we accommodate a shared encoder buffer to compensate for rate fluctuations. Although the proposed scheme is general, and it can be adopted for any video and image coding standard, we provide experimental evidence by transcoding bitstreams encoded using the state-of-the-art H.264/AVC standard. The results of our simulations reveal that is it possible to achieve distortion smoothing both in time and across the sequences, without sacrificing coding efficiency.