IF THE SENDER'S PREFERENCES are monotonic in the Receiver's action, then it is known that the Sender reveals its type in every sequential equilibrium of a Sender-Receiver game with verifiable messages (see, e.g., Milgrom (1981)). Monotonicity is a natural condition in social situations such as buyer-seller relationships; but there are obviously other situations in which the ideal action for a Sender varies with its type. Accordingly, we generalize Milgrom's result by replacing monotonicity with more general conditions on the Sender's preferences, which are sufficient for existence and uniqueness of a fully revealing equilibrium in verifiable message games. These conditions include all games in which preferences satisfy the conditions which Crawford-Sobel (1982) imposed on cheap talk games.