We show that the standard method of saturated sets for proving strong normalization of fi-reduction in the simply typed and second order polymorphic lambda calculus incorporates non-structural subtyping systems in a natural way. This shows that strong normalization for non-structural subtyping proved by Wand, O'Keefe and Palsberg [24] via coercion interpretations can be obtained in a straight-forward extension of the standard method. The proof presented here is compared to other proofs of strong normalization for subtyping systems.