We demonstrate the growth of twin-free BiTe and SbTe topological insulators by molecular beam epitaxy and a sizable reduction of the twin density in BiSe on lattice-matched BaF(111) substrates. Using X-ray diffraction, electron diffraction and atomic force microscopy, we systematically investigate the parameters influencing the formation of twin domains and the morphology of the films, and show that Se- and Te-based alloys differ by their growth mechanism. Optimum growth parameters are shown to result in intrinsically low-doped films, as probed by angle-resolved photoelectron spectroscopy. In contrast to previous approaches in which twin-free BiSe films are achieved by increasing the substrate roughness, the quality of our BiTe is superior on the flattest BaF substrates. This finding indicates that, during nucleation, the films not only interact with the topmost atomic substrate layer but also with buried layers that provide the necessary stacking information to promote a single twin, an observation that is supported by ab initio calculations.