The single-rate Erlang-B model is and has been a cornerstone of numerous traffic engineering applications which involve the calculation and optimization of blocking probabilities. However, with the emerging integrated multimedia networks, one single traffic type is often inadequate. Yet the single-rate Erlang-B model is often used even for today's new networks. A primary reason for this is the existence of methods to compute blocking probabilities and their derivatives that are simple, fast, and stable. With this paper, we provide an improved, and better, way of computing multi-rate Erlang-B blocking probabilities and their derivatives. Since the improvements are also simple, fast, direct, and stable, optimization and engineering methods based on a single-rate Erlang-B model can now be easily extended to emerging multimedia networks.