In this paper we consider semantic spaces consisting of objects from some particular domain (e.g. IMDB movie reviews). Various authors have observed that such semantic spaces often model salient features (e.g. how scary a movie is) as directions. These feature directions allow us to rank objects according to how much they have the corresponding feature, and can thus play an important role in interpretable classifiers, recommendation systems, or entity-oriented search engines, among others. Methods for learning semantic spaces, however, are mostly aimed at modelling similarity. In this paper, we argue that there is an inherent trade-off between capturing similarity and faithfully modelling features as directions. Following this observation, we propose a simple method to fine-tune existing semantic spaces, with the aim of improving the quality of their feature directions. Crucially, our method is fully unsupervised, requiring only a bag-of-words representation of the objects as input.