The tellurides of bismuth and antimony (Bi₂Te₃and Sb₂Te₃) are prominent members of the V₂VI₃material family that exhibit promising topological properties. We provide a method for the rational synthesis of mixed crystals of these materials ((Bi_xSb_1-x)₂Te₃with x = 0.1,..., 0.9) by means of a bottom-up chemical vapor transport (CVT) approach. Thermodynamic calculations showed the synthesis to be possible in the temperature range of 390-560 °C without significant enrichment of either component and without adding a transport agent. The starting materials were synthesized and verified by X-ray diffraction (XRD). Optimization experiments showed the ideal conditions for nanosheet synthesis to be T₂= 560 °C, T₁= 390 °C with a reaction time of t = 36 h. Crystals with heights of down to 12 nm (12 quintuple layers) were synthesized and analyzed by means of scanning electron microscopy, energy-dispersive X-ray spectrometry, and atomic force microscopy. High-resolution transmission electron microscopy confirmed the R3¯ m crystal structure, high crystallinity, and overall quality of the synthesized (Bi_xSb_1-x)₂Te₃nanosheets. Magnetotransport measurements revealed that such ternary compounds can have a significantly reduced carrier density compared to the binary parent compounds.