Paleontological and lithological studies of a carbonate mound provide the necessary data from which characterizations for that mound or locality can be constructed. These data-based characterizations are a convenient mechanism for making qualitative comparisons with other mounds, as has been done in some previous studies that discussed Middle Ordovician (now considered Upper Ordovician) mounds of the Appalachian Basin. Each of these studies had a different focus, including the paleoecology of individual mound localities, issues of ecological zonation, and regional stratigraphical investigation. Quantitative comparisons are precluded among these studies because each mound was sampled using different procedures, resulting in paleontological data sets of dissimilar density and depth. Two mound localities from carbonates of the Upper Ordovician Chickamauga Group (Stones River equivalent) of Jefferson and Blount counties, AL, were chosen for study to investigate the application of random sampling techniques to mound populations in outcrop. One mound from each locality was completely censused to generate population compositional and structural data. The location and higher-level identification of each macrofossil on the surface of these mounds were recorded. These bryozoan-dominated data sets represent the best estimates available concerning the underlying population of mound constructors, dwellers, and occasional "visitors." Rarefaction analysis was used to predict the number of randomly chosen fossils needed to detect the major taxonomic groups from each of these populations. A computer program (TARGET) was written to validate rarefaction predictions by conducting random sampling experiments using the census data sets. The program prompts for input of three user-defined variables that set the parameters of a sampling experiment and then throws randomly located sampling boxes at the mound data set, recording the results. Statistical analysis of results from these sampling experiments validated the predictions of rarefaction analysis and led us to employ a conservative approach for sampling additional mounds at these localities. © 2001 Elsevier Science B.V. All rights reserved.