The standard view in biology is that all animals, from bumblebees to human beings, face a trade-off between speed and accuracy as they search for resources and mates, and attempt to avoid predators. For example, the more time a forager spends out of cover gathering information about potential food sources the more likely it is to make accurate decisions about which sources are most rewarding. However, when the cost of time spent out of cover rises (e.g. in the presence of a predator) the optimal strategy is for the forager to spend less time gathering information and to accept a corresponding decline in the accuracy of its decisions. We suggest that this familiar picture is missing a crucial dimension: the amount of effort an animal expends on gathering information in each unit of time. This is important because an animal that can respond to changing time costs by modulating its level of effort per-unit-time does not have to accept the same decrease in accuracy that an animal limited to a simple speed-accuracy trade-off must bear in the same situation. Instead, it can direct additional effort towards (i) reducing the frequency of perceptual errors in the samples it gathers or (ii) increasing the number of samples it gathers per-unit-time. Both of these have the effect of allowing it to gather more accurate information within a given period of time. We use a modified version of a canonical model of decision-making (the sequential probability ratio test) to show that this ability to substitute effort for time confers a fitness advantage in the face of changing time costs. We predict that the ability to modulate effort levels will therefore be widespread in nature, and we lay out testable predictions that could be used to detect adaptive modulation of effort levels in laboratory and field studies. Our understanding of decision-making in all species, including our own, will be improved by this more ecologically-complete picture of the three-way tradeoff between time, effort per-unit-time and accuracy.