We discuss the two standard constructions used in the search for intermittency, the exclusive and inclusive scaled factorial moments. We propose the use of a new scaled factorial moment that reduces to the exclusive moment in the appropriate limit and is free of undesirable multiplicity correlations that are contained in the inclusive moment. We show that there are some similarities among most of the models that have been proposed to explain factorial-moment data, and that these similarities can be used to increase the efficiency of testing these models. We begin by calculating factorial moments from a simple independent-cluster model that assumes only approximate boost invariance of the cluster rapidity distribution and an approximate relation among the moments of the cluster multiplicity distribution. We find two scaling laws that are essentially model independent. The first scaling law relates the moments to each other with a simple formula, indicating that the different factorial moments are not independent. The second scaling law relates samples with different rapidity densities. We find evidence for much larger clusters in heavy-ion data than in light-ion data, indicating possible {ital spatial} intermittency in the heavy-ion events.