When navigating uncertain worlds, humans must balance exploring new options versus exploiting known rewards. Longer horizons and spatially structured option values encourage humans to explore, but the impact of real-world cognitive constraints such as environment size and memory demands on explore-exploit decisions is unclear. In the present study, humans chose between options varying in uncertainty during a multi-armed bandit task with varying environment size and memory demands. Regression and cognitive computational models of choice behavior showed that with a lower cognitive load, humans are more exploratory than a simulated value-maximizing learner, but under cognitive constraints, they adaptively scale down exploration to maintain exploitation. Thus, while humans are curious, cognitive constraints force people to decrease their strategic exploration in a resource-rational-like manner to focus on harvesting known rewards.