The critical path method/program evaluation and review technique method of project scheduling is based on the importance of managing a project's critical path(s). Although a critical path is the longest path through a network, its location in large projects is facilitated by the computation of activity slack. However, logical fallacies in oft-repeated statements of the relationship between slack and the critical path make it easy to overlook the phenomenon of zero-slack, noncritical paths. This article points out the fallacies and then describes and illustrates the phenomenon. We conclude with teaching recommendations to avoid suboptimal decisions in reducing project duration.