Two alternative approaches to identifying a model confidence set (MCS) are contrasted. Together with a specification of the established MCS test, we present a new version of a test that identifies a model set satisfying the MCS requirements and is characterised by an alternative model ranking p-value. We also contrast the two MCS approaches empirically, constructing a market risk model selection exercise for the Dow Jones Industrial Average. Our adapted MCS method is shown to lead to a smaller MCS, nested within the MCS determined by the popular MCS method, and allows greater distinction between models. (C) 2017 Elsevier Inc. All rights reserved.