In this paper, we study the rate constraints required for variable rate video transmission over ATM networks. Our objective is to achieve both good source quality and efficient network utilization. We show that these objectives may not be achieved simultaneously unless both network and source coding considerations are taken into account. In particular, we show that, given a rate constraint, a greedy source coding strategy will reduce the potential for statistical multiplexing gain in the network. We propose two alternative methods to achieve our goals. The fil st method requires non-greedy source coding techniques, implementable through I ate control, such that video encoders will only use the bit rate needed to achieve a certain, nearly constant quality level. As a consequence, low activity scenes will use a fraction of the maximum allowable bit rate. The second method calls for increasing the number of rate constraints imposed on each connection so that the amount of bandwidth used in the worst case (ie by greedy coders) is limited. Experimental results for a medium length (5 min) video sequence are given.