Branching in semiconductor nanocrystals, which leads to tetrapods and to more complex architectures, is the subject of intensive investigation. Here we support the model according to which branching in CdTe nanocrystals is driven by the formation of multiple wurtzite twins. This is in contrast to previous models for this material. We found that twinning, as well as anisotropic growth, can be triggered by the presence of suitable molecules, such as for instance methylphosphonic acid. In the case of CdTe nanocrystals, we designed a robust growth scheme in which the variation of a single parameter (the concentration of methylphosphonic acid in solution) leads to the controlled formation of nanocrystals with shapes ranging from spheres to anisotropic structures with varying level of branching, as both twinning and anisotropic growth are progressively favored. We believe that these concepts can be extended to other nanocrystal systems.