We revisit the canonical model of repeated games with two patient players, observable actions, and one-sided incomplete information, and make the substantive assumption that the informed player's preference is state independent. We show the informed player can attain a payoff in equilibrium if and only if she can attain it in the simple class of equilibria first studied by Aumann, Maschler, and Stearns (1968), in which the initial stages are used only for revealing information, and no further information is revealed after the initial stages. This sufficiency result does not extend to the uninformed player's equilibrium payoff set.