The prisoner's dilemma (PD) is arguably the most important model of social dilemmas, but our knowledge about how a PD's material payoff structure affects cooperation is incomplete. In this paper we investigate the effect of variation in material payoffs on cooperation, focusing on one-shot PD games where efficiency requires mutual cooperation. We report results from three experiments (N = 1,993): in a preliminary experiment, we vary the payoffs over a large range. In our first main experiment (Study 1), we present a novel design that varies payoffs orthogonally in a within-subjects design. Our second main experiment, Study 2, investigates the orthogonal variation of payoffs in a between-subjects design. In a complementary analysis we also study the closely related payoff indices of normalized loss and gain, and the K-index. The most robust finding of our experiments and the complementary analyses is that cooperation in a PD increases with the gains of mutual cooperation over mutual defection.