We give some sufficient conditions for a predicate P in a complete theory T to be "stably embedded". Let P be P with its "induced θ-definable structure". The conditions are that P (or rather its theory) is "rosy", P has NIP in T and that P is stably 1-embedded in T. This generalizes a recent result of Hasson and Onshuus [6] which deals with the case where P is o-minimal in T. Our proofs make use of the theory of strict (...) nonforking and weight in NIP theories ([3], [10]). (shrink)