The 9-dot problem is widely regarded as a difficult insight problem. The authors present a detailed information-processing model to explain its difficulty, based on maximization and progress-monitoring heuristics with lookahead. In Experiments 1 and 2, the model predicted performance for the 9-dot and related problems. Experiment 3 supported an extension of the model that accounts for insightful moves. Experiments 4 and 5 provided a critical test of model predictions versus those of previous accounts. On the basis of these findings, the authors claim that insight problem solving can be modeled within a means-ends analysis framework. Maximization and progress-monitoring heuristics are the source of problem difficulty, but also create the conditions necessary for insightful moves to be sought. Furthermore, they promote the discovery and retention of promising states that meet the progress-monitoring criterion and attenuate the problem space.