Automatic composition of semantic web services should make use of the ontology in which the services are specified. While the approaches can strongly benefit from doing so, they have to deal with the frame and ramification problems, necessitating worst-case exponential reasoning even to determine the outcome of applying a single web service. The existing approaches to composition either ignore the background ontology, matching web services based on concept names and hence removing the need for reasoning; or they employ full-scale reasoning and suffer from the unavoidable performance deficiencies. In our work, we instead look for interesting classes of ontologies where the required reasoning is polynomial. We define a formalism for semantic web service composition. We present polynomial-time methods for dealing with several of the most commonly used ontology modelling constructs; further extensions are possible. We prove that our methods are correct. We are currently developing an implementation of our techniques.