In many domains of cognitive psychology, it is proposed that people are equipped with a repertoire of strategies to solve the problems they face. For instance, it is proposed that when people use multiple cues to make a probabilistic inference about a criterion, they sometimes rely on simple heuristics and sometimes apply more elaborate additive strategies. Indeed, many studies suggest that people’s inferences can be described by different strategies in different situations. However, critics of this view suggest that people do not apply different strategies but instead adjust one single strategy to the characteristics of each situation. Here we examine the strategies that individuals use when available resources change. Therefore, we continuously change the cost of deliberation time. The behavior of participants at the transition from fast and simple behavior to slow but optimal information integration offers insight into whether people select different strategies or continuously adjust one single strategy.