This paper presents the submissions by the University of Zurich to the\nSIGMORPHON 2017 shared task on morphological reinflection. The task is to\npredict the inflected form given a lemma and a set of morpho-syntactic\nfeatures. We focus on neural network approaches that can tackle the task in a\nlimited-resource setting. As the transduction of the lemma into the inflected\nform is dominated by copying over lemma characters, we propose two recurrent\nneural network architectures with hard monotonic attention that are strong at\ncopying and, yet, substantially different in how they achieve this. The first\napproach is an encoder-decoder model with a copy mechanism. The second approach\nis a neural state-transition system over a set of explicit edit actions,\nincluding a designated COPY action. We experiment with character alignment and\nfind that naive, greedy alignment consistently produces strong results for some\nlanguages. Our best system combination is the overall winner of the SIGMORPHON\n2017 Shared Task 1 without external resources. At a setting with 100 training\nsamples, both our approaches, as ensembles of models, outperform the next best\ncompetitor.\n