Location-allocation models based on optimization criteria are appropriate tools for the analysis of archaeological settlement patterns. In early agricultural societies, elite classes might maximize their control of the population and resources by optimally situating their primary settlements. Location-allocation models can simulate the multiple factors that potentially underlie settlement site location decisions. I describe several maximal covering models and their applicability to understand the degree of political centralization in the Upper Tennessee River Valley during several Mississippian archaeological cultural phases (900 to 1600 A.D.). My results support the notion that the main objective of the Mississippian elite in choosing sites for administrative centers was to maximize control of the local population and the supporting agricultural economy. The results also support the work of anthropologists and archaeologists regarding the variable degrees of political complexity during time periods of the Mississippian culture. Cultures during the earliest time period (1000-1200 A.D.) and the northern part of the study area during the latest time period (1450-1600 A.D.) in the analysis were found to be the least complex, resembling simple tribal societies unable to maximize their control over the entire Valley population and its resources. Factors such as the location of trade routes and selected resource deposits were not accounted for in the location-allocation models developed for this research and may account for the less-than-optimal results in settlement system control.