Abstract: Many NLP applications, such as biomedical data and technical support, have 10-100 million tokens of in-domain data and limited computational resources for learning from it. How should we train a language model in this scenario? Most language modeling research considers either a small dataset with a closed vocabulary (like the standard 1 million token Penn Treebank), or the whole web with byte-pair encoding. We show that for our target setting in English, initialising and freezing input embeddings using in-domain data can improve language model performance by providing a useful representation of rare words, and this pattern holds across several different domains. In the process, we show that the standard convention of tying input and output embeddings does not improve perplexity when initializing with embeddings trained on in-domain data.