In this paper, we consider the problem of rate control for video transmission. We focus on finding off-line optimal rate control for constant bit-rate (CBR) transmission, where the size of the encoder buffer and the channel rate are the constraints. To ensure a maximum minimum quality is obtained over all data units (e.g., macro blocks, video frames or group-of-pictures), we use a minimum maximum distortion (MMAX) criterion for this buffer-constrained problem. We show that, due to the buffer constraints, a MMAX solution leads to a relatively low average distortion, because the total rate budget is not completely utilized. Therefore, after finding a MMAX solution, an additional minimization of average distortion criterion is proposed to increase overall quality of the data sequence by using remaining resources. The proposed algorithm (denoted MMAX+ as it incorporates both MMAX and the additional average quality optimization stage) leads to an increase in average quality with respect to the MMAX solution, while providing a much more constant quality than MMSE solutions. Moreover we show how the MMAX+ approach can be implemented with low complexity.