State-of-the-art methods for Word Sense Disambiguation (WSD) combine two different features: the power of pre-trained language models and a propagation method to extend the coverage of such models. This propagation is needed as current sense-annotated corpora lack coverage of many instances in the underlying sense inventory (usually WordNet). At the same time, unambiguous words make for a large portion of all words in WordNet, while being poorly covered in existing sense-annotated corpora. In this paper we propose a simple method to provide annotations for most unambiguous words in a large corpus. We introduce the UWA (Unambiguous Word Annotations) dataset and show how a state-of-the-art propagation-based model can use it to extend the coverage and quality of its word sense embeddings by a significant margin, improving on its original results on WSD.