An algorithm is proposed to determine antecedents for VP ellipsis. The algorithm eliminates impossible antecedents, and then imposes a preference ordering on possible antecedents. The algorithm performs with 94% accuracy on a set of 304 examples of VP ellipsis collected from the Brown Corpus. The problem of determining antecedents for VP ellipsis has received little attention in the literature, and it is shown that the current proposal is a significant improvement over alternative approaches.