Most state-of-the-art wide-coverage parsers are trained on newspaper text and suffer a loss of accuracy in other domains, making parser adaptation a pressing issue. In this paper we demonstrate that a CCG parser can be adapted to two new domains, biomedical text and questions for a QA system, by using manually-annotated training data at the POS and lexical category levels only. This approach achieves parser accuracy comparable to that on newspaper data without the need for annotated parse trees in the new domain. We find that retraining at the lexical category level yields a larger performance increase for questions than for biomedical text and analyze the two datasets to investigate why different domains might behave differently for parser adaptation.