Scholars studying human organizations have recently adopted the notion of fitness landscapes, a concept pioneered in the biological and physical sciences. Such scholars have generally assumed that organizations will migrate toward the local peaks of these landscapes, as biological and physical entities do. We use an agent-based simulation to show, to the contrary, that a hierarchical human organization may very well come to rest at a "sticking point" which is not a local peak on the fitness landscape of the overall organization. Three pervasive features of human organizations create the distinction between sticking points and local peaks: the delegation of choices to distinct decision makers, independencies between the domains of those decision makers, and differences between local incentives and global incentives. Our results illustrate both that it is valuable to use tools developed to study one type of complex adaptive system in order to examine another type and that researchers must adapt the tools with care as they attempt to do so.