Self-ordered three-dimensional body-centered tetragonal (BCT) SiGe nanodot structures are fabricated by depositing SiGe/Si superlattice layer stacks using reduced pressure chemical vapor deposition. For high enough Ge content in the island (>30%) and deposition temperature of the Si spacer layers (T > 700 °C), we observe the formation of an ordered array with islands arranged in staggered position in adjacent layers. The in plane periodicity of the islands can be selected by a suitable choice of the annealing temperature before the Si spacer layer growth and of the SiGe dot volume, while only a weak influence of the Ge concentration is observed. Phase-field simulations are used to clarify the driving force determining the observed BCT ordering, shedding light on the competition between heteroepitaxial strain and surface-energy minimization in the presence of a non-negligible surface roughness.