Algorithms for composing Web services (WS) traditionally utilize the functional and quality-of-service parameters of candidate services to decide which services to include in the composition. Users often have differing experiences with a WS. While trust in a WS is multi-faceted and consists of security and behavioral aspects, our focus in this paper is on the latter. We adopt a formal model for trust in a WS, which meets many of our intuitions about trustworthy WSs. We hypothesize predictors of a positive experience with a WS and conduct a small pilot study to explore correlations between subjects' experiences with WSs in a composition and the predictor values for those WSs. Furthermore, we show how we may derive trust for compositions from trust models of individual services. We conclude by presenting and evaluating a novel framework, called Wisp, that utilizes the trust models and, in combination with any WS composition tool, chooses compositions to deploy that are deemed most trustworthy.