In this article, we report a surprising phenomenon: Oblique CF-varimax and oblique CF-quartimax rotation produced similar point estimates for rotated factor loadings and factor correlations but different standard error estimates in an empirical example. Influences of factor rotation on asymptotic standard errors are investigated using a numerical exploration method. The results are (a) CF-varimax, CF-quartimax, CF-equamax, and CF-parsimax produced similar asymptotic standard errors when the factor loading matrix is an independent cluster solution and (b) the four rotation methods produced different asymptotic standard errors when the factor loading matrix has a more complex structure. In addition, properties of the CF family are explored with a full range of ? values.