This paper presents the Instituto de Telecomunicações–Instituto Superior Técnico submission to Task 1 of the SIGMORPHON 2019 Shared Task. Our models combine sparse sequence-to-sequence models with a two-headed attention mechanism that learns separate attention distributions for the lemma and inflectional tags. Among submissions to Task 1, our models rank second and third. Despite the low data setting of the task (only 100 in-language training examples), they learn plausible inflection patterns and often concentrate all probability mass into a small set of hypotheses, making beam search exact.