We present Finesse, a system that forms plans for declarer play in the game of Bridge. Finesse generalises the technique of proof-planning, developed at Edinburgh University in the context of mathematical theorem-proving, to deal with the disjunctive choice encountered when planning under uncertainty, and the context-dependency of actions produced by the presence of an opposition. In its domain of planning for individual suits, it correctly identified the proper lines of play found in many examples from the Bridge literature, supporting its decisions with probabilistic and qualitative information. Cases were even discovered in which Finesse revealed errors in the analyses presented by recognised authorities.