Abstract Many common character-level, string-tostring transduction tasks, e.g. graphemeto-phoneme conversion and morphological inflection, consist almost exclusively of monotonic transduction. Neural sequence-tosequence models with soft attention, which are non-monotonic, often outperform popular monotonic models. In this work, we ask the following question: Is monotonicity really a helpful inductive bias in these tasks? We develop a hard attention sequence-to-sequence model that enforces strict monotonicity and learns a latent alignment jointly while learning to transduce. With the help of dynamic programming, we are able to compute the exact marginalization over all monotonic alignments. Our models achieve state-of-the-art performance on morphological inflection. Furthermore, we find strong performance on two other character-level transduction tasks. Code is available at https://github.com/ shijie-wu/neural-transducer