<p>Liquid crystal elastomers (LCEs) are actuating soft solids that exhibit large and reversible contractions along the liquid crystal director on heating through the nematic-isotropic transition. Recently, mechanical programming was used to fabricate LCEs that can actuate into arbitrarily complex shapes such as a face. Here, we combine theoretical and experimental observations to explain how such complex mechanical programming works. Crucially, we identify the intermediate pre-programmed state as an isotropic genesis polydomain, which, during programming, can accommodate the imposed strains via a pure soft-mode response enabled by director rotation and laminar microstructures. Second cross-linking fixes these microstructures as preferred but, since they were achieved softly, they do not involve any reconfiguration of the isotropic state, allowing it to be restored on heating. Experimental observations of programmed LCEs reveal both single and double laminate structures, as anticipated by the theory, and also a quantitative match between the 3D deformations that can and cannot be programmed. The set of programmable deformations includes all modest isochoric deformations, explaining why arbitrary shape programming works. Finally, we demonstrate theoretically and experimentally that programming also allows one to engineer samples with desired extents of softness in different directions.</p>