Abstract : We present work-in-progress on type inference in presence of type-directed name disambiguation (where an ambiguous name is resolved using type information), following the approach of constraint-based type inference. Our specific goal is to implement inference for OCaml sum/variant constructor disambiguation, and our approach is to introduce "frozen constraints", a more general constraint mechanism. We have a prototype implementation of frozen constraints in the Inferno library, and discuss the implementation and meta-theoretical challenges.