Labeled types and a new relation between types are added to the lambda calculus of objects as described in [5]. This relation is a trade-off between the possibility of having a restricted form of width subtyping and the features of the delegation-based language itself. The original type inference system allows both specialization of the type of an inherited method to the type of the inheriting object and static detection of errors, such as 'message-not-understood'. The resulting calculus is an extension of the original one. Type soundness follows from the subject reduction property.