Humans frequently cooperate for collective benefit, even in one-shot social dilemmas. This provides a challenge for theories of cooperation. Two views focus on intuitions but offer conflicting explanations. The Social Heuristics Hypothesis argues that people with selfish preferences rely on cooperative intuitions and predicts that deliberation reduces cooperation. The Self-Control Account emphasizes control over selfish intuitions and is consistent with strong reciprocity—a preference for conditional cooperation in one-shot dilemmas. Here, we reconcile these explanations with each other as well as with strong reciprocity. We study one-shot cooperation across two main dilemma contexts, provision and maintenance, and show that cooperation is higher in provision than maintenance. Using time-limit manipulations, we experimentally study the cognitive processes underlying this robust result. Supporting the Self-Control Account, people are intuitively selfish in maintenance, with deliberation increasing cooperation. In contrast, consistent with the Social Heuristics Hypothesis, deliberation tends to increase the likelihood of free-riding in provision. Contextual differences between maintenance and provision are observed across additional measures: reaction time patterns of cooperation; social dilemma understanding; perceptions of social appropriateness; beliefs about others’ cooperation; and cooperation preferences. Despite these dilemma-specific asymmetries, we show that preferences, coupled with beliefs, successfully predict the high levels of cooperation in both maintenance and provision dilemmas. While the effects of intuitions are context-dependent and small, the widespread preference for strong reciprocity is the primary driver of one-shot cooperation. We advance the Contextualised Strong Reciprocity account as a unifying framework and consider its implications for research and policy.