How does cognitive sophistication impact cooperation? We explore this question using a model of the co-evolution of cooperation and cognition. In our model, agents confront social dilemmas and coordination games, and make decisions using intuition or deliberation. Intuition is automatic and effortless, but relatively (although not necessarily completely) insen- sitive to context. Deliberation, conversely, is costly but relatively (although not necessarily perfectly) sensitive to context. We find that regardless of the sensitivity of intuition and imperfection of deliberation, deliberating undermines cooperation in social dilemmas, whereas deliberating can increase cooperation in coordination games if intuition is sufficiently sensitive. Furthermore, when coordination games are sufficiently likely, selection favours a strategy whose intuitive response ignores the contextual cues available and cooperates across contexts. Thus, we see how simple cog- nition can arise from active selection for simplicity, rather than just be forced to be simple due to cognitive constraints. Finally, we find that when delib- eration is imperfect, the favoured strategy increases cooperation in social dilemmas (as a result of reducing deliberation) as the benefit of cooperation to the recipient increases.