Speech recognition systems that combine multiple types of acoustic models have been shown to outperform single-model systems. However, such systems can be complex to implement and too resource-intensive to use in production. This paper describes how to use knowledge distillation to combine acoustic models in a way that has the best of all worlds: It improves recognition accuracy significantly, can be implemented with standard training tools, and requires no additional complexity during recognition. First, we identify a simple but particularly strong type of ensemble: a late combination of recurrent neural networks with different architectures and training objectives. To harness such an ensemble, we use a variant of standard cross-entropy training to distill it into a single model and then discriminatively fine-tune the result. An evaluation on 2,000-hour large vocabulary tasks in 5 languages shows that the distilled models provide up to 8.9% WER improvement over conventionally-trained baselines, despite having an identical number of parameters.