As recurrent neural networks become larger and deeper, training times for single networks are rising into weeks or even months. As such there is a significant incentive to improve the performance and scalability of these networks. While GPUs have become the hardware of choice for training and deploying recurrent models, the implementations employed often make use of only basic optimizations for these architectures. In this article we demonstrate that by exposing parallelism between operations within the network, an order of magnitude speedup across a range of network sizes can be achieved over a naive implementation. We describe three stages of optimization that have been incorporated into the fifth release of NVIDIA's cuDNN: firstly optimizing a single cell, secondly a single layer, and thirdly the entire network.