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In this initial simulation study, we propose and evaluate a method for exploratory measurement model discovery that utlizes the simulated annealing algorithm, previously used for other model selection problems, to search for confirmatory factor analysis models that fit the data. We compare using BIC and CFI as objective functions for the SA algorithm across 24 combinations of number of items (3 levels), observations per item (2 levels), and correlations between latent factors (2 levels). BIC recovered both the number and structure of the latent factors most accurately in the conditions with fewer items, with its accuracy falling as more items were included while CFI had somewhat more stable but lower peak accuracy across conditions. Further study conditions are described.