As conveyed in the original derivation and subsequent extensions, the justification of SIC is based on establishing that the criterion serves as an asymptotic approximation to a transformation of the Bayesian posterior probability of a candidate model. Our interest lies in investigating this justification for the possibility of retaining terms in the criterion which are asymptotically negligible. Such terms would be of debatable value in large- sample settings, but may improve the effectiveness of SIC in small to moderate sample-size applications.