Ultra-fine entity typing (UFET) is the task of inferring the semantic types, from a large set of fine-grained candidates, that apply to a given entity mention. This task is especially challenging because we only have a small number of training examples for many of the types, even with distant supervision strategies. State-of-the-art models, therefore, have to rely on prior knowledge about the type labels in some way. In this paper, we show that the performance of existing methods can be improved using a simple technique: we use pre-trained label embeddings to cluster the labels into semantic domains and then treat these domains as additional types. We show that this strategy consistently leads to improved results, as long as high-quality label embeddings are used. We furthermore use the label clusters as part of a simple post-processing technique, which results in further performance gains. Both strategies treat the UFET model as a black box and can thus straightforwardly be used to improve a wide range of existing models.