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Bifactor-(S-1) and (S∙I-1) models represent respecified General (G)-factor measurement models intended to overcome noted anomalous results associated with bifactor models. Current research has centered on model utility within applied studies, with little consideration of conditions (e.g., sample size) associated with parameter recovery accuracy, including their predictive utility. This simulation study investigated the parameter recovery of bifactor-(S-1) and (S∙I-1) models under varying conditions. Particular emphasis is the recovery of the regression coefficient specifying the relationship of the bifactor primary dimension to an external criterion. Furthermore, regression coefficient recovery was compared to results based on a unidimensional model to examine the consequences associated with ignoring an instrument’s multidimensional structure. Implications to research and practice are discussed.