Research on computational models of scientific discovery investigates both the induction of descriptive laws and the construction of explanatory models. Although the work in law discovery centers on knowledge-lean approaches to searching a problem space, research on deeper modeling tasks emphasizes the pivotal role of domain knowledge. As an example, our own research on inductive process modeling uses information about candidate processes to explain why variables change over time. However, our experience with IPM, an artificial intelligence system that implements this approach, suggests that process knowledge is insufficient to avoid consideration of implausible models. To this end, the discovery system needs additional knowledge that constrains the model structures. We report on an extended system, SC-IPM, that uses such information to reduce its search through the space of candidates and to produce models that human scientists find more plausible. We also argue that although people carry out less extensive search than SC-IPM, they rely on the same forms of knowledge—processes and constraints—when constructing explanatory models.