We combine two complementary ideas for learning supertaggers from highly ambiguous lexicons: grammar-informed tag transitions and models minimized via integer programming. Each strategy on its own greatly improves performance over basic expectation-maximization training with a bitag Hidden Markov Model, which we show on the CCGbank and CCG-TUT corpora. The strategies provide further error reductions when combined. We describe a new two-stage integer programming strategy that efficiently deals with the high degree of ambiguity on these datasets while obtaining the full effect of model minimization.