  So called pair copula constructions (PCCs), specifying multivariate
distributions only in terms of bivariate building blocks (pair copulas),
constitute a flexible class of dependence models. To keep them tractable for
inference and model selection, the simplifying assumption that copulas of
conditional distributions do not depend on the values of the variables which
they are conditioned on is popular. In this paper, we show for which classes of
distributions such a simplification is applicable, significantly extending the
discussion of Hob{\ae}k Haff et al. (2010). In particular, we show that the
only Archimedean copula in dimension d \geq 4 which is of the simplified type
is that based on the gamma Laplace transform or its extension, while the
Student-t copula is the only one arising from a scale mixture of Normals.
Further, we illustrate how PCCs can be adapted for situations where conditional
copulas depend on values which are conditioned on.
