Recent research has reported successful training interventions that improve insight problem solving. In some ways this is surprising, because the processes involved in insight solutions are often assumed to be unconscious, whereas the training interventions focus on conscious cognitive strategies. We propose one mechanism that may help to explain this apparent disconnect. Recognition of a barrier to progress during insight problem solving may provide a point of access to the tacit constraining assumptions that have misled the solution process. We tested this proposal in an experiment that examined the effects of different training routines on problem solving. The experiment compared four training routines, focusing either on barriers and assumptions combined, barriers alone, assumptions alone, or goals, with two control conditions. Outcomes were measured using eleven spatial insight problems. The results indicated that training that combined focus on barriers and assumptions was significantly more effective than all other conditions, supporting the proposition that recognizing and reinterpreting barriers may assist in surfacing the unwarranted assumptions that prevent problem solving.