PURPOSE: Capture-recapture methods estimate the size of hidden populations by leveraging the proportion of overlap of the population on independent lists. Log-linear modeling relaxes the assumption of list independence, but best model selection criteria remain uncertain. Incorrect model selection can deliver incorrect and even implausible size estimates. METHODS: We used simulations to model when capture-recapture methods deliver biased or unbiased estimates and compare model selection criteria. Simulations included five scenarios for list dependence among three incomplete lists of population of interest. We compared metrics of log-linear model selection, accuracy, and precision. We also compared log-linear model performance to the decomposable graph approach (a Bayesian model average), the sparse multiple systems estimation (SparseMSE) approach that accounts for zero or low cell counts, and the Sample Coverage approach. RESULTS: Log-linear models selected by Akaike's information criterion (AIC) calculated accurate population size estimates in all scenarios except for those with sparse or zero cell counts. In these scenarios, the decomposable graph and the Sample Coverage models produced more accurate size estimates. CONCLUSIONS: Conventional capture-recapture model selection fails with sparse cell counts. This naïve approach to model selection should be replaced with the implementation of multiple different models in order triangulate the truth in real-world applications.