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Geometric constraint models (GCMs) may be important tools for understanding macroecological patterns. However, there are currently a wide range of models in use, and few established criteria for selecting a model to use in a particular case. I propose a model selection procedure that uses multiple macroecological patterns to select the best fitting GCM. I then demonstrate this method by comparing the fit of three GCMs to patterns of richness, range size and range shape of New World birds and mammals. Which GCM fit best depended on the average range size of the group in question, suggesting that the choice of which GCM to use can and should be context-dependent. Objective model-selection criteria, such as those proposed here, offer a promising basis for making this choice.