This paper presents a procedure that refines the set of equilibria in a model of cheap-talk communication. Starting with a standard cheap-talk game, the procedure assumes that the other player uses monotonic strategies and then applies iterative deletion of weakly dominated strategies. In the resulting game, if the informed player’s optimal action is uniformly higher than the uninformed player’s optimal action (under full information), then the informed player uses only the highest messages. The procedure selects the outcome with the maximal number of induced actions in prominent cases and the meaning of messages in equilibrium is fully determined.  The paper argues that the monotonicity condition it imposes on strategies is a weak and natural way to impose exogenous meaning of language in a strategic model of communication.