Abstract. We investigate the issue of typing confidentiality in a languagebased information-flow security approach, aiming at improving some previously proposed type systems, especially for higher-order languages with mutable state `a la ML. We show that the typing of terminations leaks can be largely improved, by particularizing the case where the alternatives in a conditional branching both terminate. Moreover, we also provide a quite precise way of approximating the confidentiality level of an expression, that ignores the level of values used for side-effects only.