Abduction is one of the most important forms of reasoning; it has been successfully applied to several practical problems, such as diagnosis. In this article we investigate whether the computational complexity of abduction can be reduced by an appropriate use of preprocessing. This is motivated by the fact that part of the data of the problem (namely, the set of all possible assumptions and the theory relating assumptions and manifestations) is often known before the rest of the problem. In this article, we show some complexity results about abduction when compilation is allowed.