This paper addresses two issues: how to choose between solutions for a prob
lem specified by multiple criteria, and how to search for solutions in such
situations. We argue against an approach common in decision theory, reduci
ng several criteria to a single 'cost' (e.g., using a weighted sum cost fun
ction) and instead propose a way of partially ordering solutions satisfying
a set of prioritised soft constraints. We describe a generalisation of the
A* search algorithm which uses this ordering and prove that under certain
reasonable assumptions the algorithm is complete and optimal.