Humans often seek information to minimize the pervasive effect of uncertainty on decisions. Current theories explain how much knowledge people should gather before a decision, based on the cost-benefit structure of the problem at hand. Here, we demonstrate that this framework omits a crucial agent-related factor: the cognitive effort expended while collecting information. Using an active sampling model, we unveil a speed-efficiency trade-off whereby more informative samples take longer to find. Crucially, under sufficient time pressure, humans can break this trade-off, sampling both faster and more efficiently. Computational modelling demonstrates the existence of a cost of cognitive effort which, when incorporated into theoretical models, provides a better account of people's behaviour and also relates to self-reported fatigue accumulated during active sampling. Thus, the way people seek knowledge to guide their decisions is shaped not only by task-related costs and benefits, but also crucially by the quantifiable computational costs incurred.