In this paper the homogeneity ansatz is imposed at the level of Einstein's equations and/or at the level of the action. The commutativity of these operations, as far as the resulting equations are concerned, is reinvestigated. The main result obtained is that, when the restrictions imposed by the isometry group are supplemented by the restrictions on the time-dependent matrix on the spatial part of the metric, there can be class-A space-times for which the two abovementioned procedures do not commute; there can also be class-B space-times which have valid Lagrangians. As a by-product, the compatibility of the diagonal ansatz with Einstein's field equations is revisited.