The structure determination of two composite compounds in the Zn-Pd system with close relationships to the cubic gamma-brass structure Zn11-delta Pd2+delta is reported. Their structures have been solved from single crystal X-ray diffraction data within a (3 + 1)-dimensional [(3 + 1)D] formalism. Zn75.7(7)Pd24.3 and Zn78.8(7)Pd21.2 crystallize with orthorhombic symmetry, superspace group Xmmm(00 gamma)0s0 (X [(1/2,1/2,0,0); (0,1/2,1/2,1/2); (1/2,0,1/2,1/2)]), with the following lattice parameters, respectively: a(s) = 12.929(3) angstrom, b(s) = 9.112(4) angstrom, c(s) = 2.5631(7) angstrom, q = 8/13 c* and V-s = 302.1(3) angstrom(3) and a(s) = 12.909(3) angstrom, b(s) = 9.115(3) angstrom, c(s) = 2.6052(6) angstrom, q = 11/18 c* and V-s = 306.4(2) angstrom(3). Their structures may be considered as commensurate because they can be refined in the conventional 3D space groups (Cmce and Cmcm, respectively) using supercells, but they also refined within the (3 + 1)D formalism to residual factors R = 3.14% for 139 parameters and 1184 independent reflections for Zn75.7(7)Pd24.3 and R = 3.16% for 175 parameters and 1804 independent reflections for Zn78.8(7)Pd21.2. The use of the (3 + 1)D formalism improves the results of the refinement and leads to a better understanding of the complexity of the atomic arrangement through the various modulations (occupation waves and displacive waves). Our refinements emphasize a unique Pd/Zn occupancy modulation at the center of distorted icosahedra, a modulation which correlates with the distortion of these polyhedra.