Composition models of distributional semantics are used to construct phrase representations from the representations of their words. Composition models are typically situated on two ends of a spectrum. They either have a small number of parameters but compose all phrases in the same way, or they perform word-specific compositions at the cost of a far larger number of parameters. In this paper we propose transformation weighting (TransWeight), a composition model that consistently outperforms existing models on nominal compounds, adjective-noun phrases, and adverb-adjective phrases in English, German, and Dutch. TransWeight drastically reduces the number of parameters needed compared with the best model in the literature by composing similar words in the same way.