In this work, we customized a neural machine translation system for translation of subtitles in the domain of entertainment. The neural translation model was adapted to the subtitling content and style and extended by a simple, yet effective technique for utilizing inter-sentence context for short sentences such as dialog turns. The main contribution of the paper is a novel subtitle segmentation algorithm that predicts the end of a subtitle line given the previous word-level context using a recurrent neural network learned from human segmentation decisions. This model is combined with subtitle length and duration constraints established in the subtitling industry. We conducted a thorough human evaluation with two post-editors (English-to-Spanish translation of a documentary and a sitcom). It showed a notable productivity increase of up to 37% as compared to translating from scratch and significant reductions in human translation edit rate in comparison with the post-editing of the baseline non-adapted system without a learned segmentation model.