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, focussing on one-shot PD games where efficiency requires mutual cooperation. Following Mengel (2018) we vary three payoff indices, which are each based on two payoff parameters only and therefore allow for ceteris paribus comparisons. Indices of risk and temptation capture the unilateral incentives to defect against defectors and cooperators respectively, while an index of efficiency captures the gains from cooperation. We conduct three studies (N=1,993): first, varying the payoff indices over a large range; second, in a novel orthogonal design that allows us to measure the effect of one payoff index while holding the others constant in a within-subjects design; and third in a between-subjects design. In the second study we also compare a student and non-student subject pool, which allows us to assess generalizability of results. In Studies 1 and 2 we find that temptation reduces cooperation – an effect that disappears in Study 3. Risk matters in none of the studies. As robustness checks we also investigate the closely related payoff indices of normalised loss and gain, and the K-index. The most robust finding that emerges from our three studies and the robustness checks is that cooperation in a PD increases with efficiency.