The phase diagram of the spin 1/2 XXZ model is examined for two different geometries, which can be changed from two- to three-dimensional. The first of these consists of an infinite stack of simple quadratic layers with a variable inter-layer coupling, where the ratio of the inter-layer and intra-layer couplings varies between zero and one. Second, the authors consider a slab geometry consisting of n such layers, with equal couplings in all directions. For both geometries they use the cluster variation method for two-spin clusters to construct the phase diagram of the model, and they examine the changes that take place as the system changes from two- to three-dimensional. For the slab geometry they also calculate the order parameter profile near T_c. It turns out that Dirichlet boundary conditions for the related superfluid wavefunction are most realistic.