In cheap talk games, equilibrium refinements usually start from a supposedly played equilibrium, and consider the incentives of some types to separate off path from the types they are pooled with. We take the opposite direction. We propose algorithms that start from a fully separating strategy, and merge types until an equilibrium is reached. These algorithms were first conceived to establish the existence of a perfect Bayesian equilibrium in sender-receiver games with sender’s approval in which the utility functions are single-peaked and single-crossing. When the sender’s approval is not an issue, our algorithms achieve a unique equilibrium, which fulfills many standard refinement criteria.