In repeated principal-agent problems and games, more outcomes are implementable when performance signals are privately observed by a principal or mediator with commitment power than when the same signals are publicly observed and form the basis of a recursive equilibrium. We investigate the gains from non-recursive equilibria (e.g., “review strategies”) based on privately observed signals. Under a pairwise identifiability condition, we find that the gains from non-recursive equilibria are “small”: their inefficiency is of the same 1-δ power order as that of recursive equilibria. Thus, while private strategies or monitoring can outperform public ones for a fixed discount factor, they cannot accelerate the power rate of convergence to the efficient payoff frontier when the folk theorem holds. An implication is that the gains from withholding performance feedback from agents are small when the parties are patient.