In 3D topological insulators achieving a genuine bulk-insulating state is an important research topic. Recently, the material system (Bi,Sb)2(Te,Se)3 (BSTS) has been proposed as a topological insulator with high resistivity and a low carrier concentration (Ren et al 2011 Phys. Rev. B 84 165311). Here we present a study to further refine the bulk-insulating properties of BSTS. We have synthesized BSTS single crystals with compositions around x = 0.5 and y = 1.3. Resistance and Hall effect measurements show high resistivity and record low bulk carrier density for the composition Bi Sb Te Se . The analysis of the resistance measured for crystals with different thicknesses within a parallel resistor model shows that the surface contribution to the electrical transport amounts to 97% when the sample thickness is reduced to 1 m. The magnetoconductance of exfoliated BSTS nanoflakes shows 2D weak antilocalization with as expected for transport dominated by topological surface states.