We report a general synthetic approach to tetrapod-shaped colloidal nanocrystals made of various combinations of II-VI semiconductors. Uniform tetrapods were prepared using preformed seeds in the sphalerite structure, onto which arms were grown by coinjection of the seeds and chemical precursors into a hot mixture of surfactants. By this approach, a wide variety of core materials could be chosen (in practice, most of the II-VI semiconductors that could be prepared in the sphalerite phase, namely, CdSe, ZnTe, CdTe); in contrast, the best materials for arm growth were CdS and CdTe. The samples were extensively characterized with the aid of several techniques.