Judgments and decisions under uncertainty are frequently linked to a prior sequential search for relevant information. In such cases, the subject has to decide when to stop the search for information. Evidence accumulation models from social and cognitive psychology assume an active and sequential information search until enough evidence has been accumulated to pass a decision threshold. In line with such theories, we conceptualize the evidence threshold as the “desired level of confidence” (DLC) of a person. This model is tested against a fixed stopping rule (one-reason decision making) and against the class of multi-attribute information integrating models. A series of experiments using an information board for horse race betting demonstrates an advantage of the proposed model by measuring the individual DLC of each subject and confirming its correctness in two separate stages. In addition to a better understanding of the stopping rule (within the narrow framework of simple heuristics), the results indicate that individual aspiration levels might be a relevant factor when modelling decision making by task analysis of statistical environments.