We investigate a general subset of 2D, orthogonal, compactly supported wavelets. This subset, which has a simple parameterization, includes all wavelets with a corresponding wavelet (polyphase) matrix, that can be factored as a product of factors of degree--1, in one variable. In this paper we consider a particular wavelets with vanishing moments. The number of vanishing moments that can be achieved increases with the increase of the McMillan degrees of the wavelet matrix. We design wavelets with the maximal number of vanishing moments for given McMillan degrees, by solving a set of nonlinear constraints, and discuss their relation to regular, smooth wavelets. Design examples are given for two fundamental sampling schemes, the quincunx and the four-band separable sampling.