Most machine translation systems construct translations from a closed vocabulary of target word forms, posing problems for translating into languages that have productive compounding processes. We present a simple and effective approach that deals with this problem in two phases. First, we build a classifier that identifies spans of the input text that can be translated into a single compound word in the target language. Then, for each identified span, we generate a pool of possible compounds which are added to the translation model as “synthetic” phrase translations. Experiments reveal that (i) we can effectively predict what spans can be compounded; (ii) our compound generation model produces good compounds; and (iii) modest improvements are possible in end-to-end English–German and English–Finnish translation tasks. We additionally introduce KomposEval, a new multi-reference dataset of English phrases and their translations into German compounds.