Qualified types provide a general framework for constrained type systems, with applications including type class overloading, subtyping and record calculi. This paper presents an extended version of the type inference algorithm used in previous work, that can take account of the satisfiability of constraints to obtain more accurate principaf types, The new algorithm is obtained by adding two new rules, one for sirnpltficatirm and one for m~ prowwnent of constraint sets. In particular, it permits a better treatment of the previously troublesome multiple parameter extensions of Haskell type classes, generalizing the system of parometrzc typf clo. sses proposed by Chen, Hudak and Odersky.