The composite voxel method [1, 2] permits state-of-the-art FFT-based computational mi- cromechanics to be accelerated by providing a surrogate constitutive law for heterogeneous voxels arising during coarsening of a fine voxel grid or when the microstructure is given analytically. Subsequent research [3, 4, 5] proposed strategies for handling general inelas- tic and potentially finite strain mechanics. Motivated by the unreasonable effectiveness of the composite voxel technique, we wondered about a more fundamental reason for its success. We provide a natural derivation of the laminate composite voxel technique as an assumed strain method by showing that the composite voxel method may be embedded into the general FE framework introduced by Simo-Rifai [6] for a particular choice of extended strain field. Instead of a judiciously constructed constitutive law, as originally assumed, the composite voxel method arises from a kinematic assumption within a discretization scheme. In addition, we discuss approaches for integrating composite voxels into an existing level- set framework used to describe heterogeneous microstructures. The focus of our approach is on the efficient and accurate computation of normal vectors and cut-volume fractions of composite voxels.