Quantum wells of InGaSb clad by AlGa(As)Sb were grown by molecular beam epitaxy. Well and barrier compositions were chosen to yield biaxial compressive strain and enhanced hole mobility in the InGaSb. Wells with thickness of 7.5 nm exhibited room-temperature mobilities of 1000 cm 2 /V s to 1100 cm 2 / V s, with the surface-layer material influencing two-dimensional hole densities. The introduction of As into the barrier material allows a wider range of p-channel well/barrier combinations and lattice constants. These could be compatible with n-channel InGaAs wells for complementary field-effect transistor circuits which utilize a common buffer layer. InGaSb wells with thicknesses of 20 nm to 30 nm and compressive strains of 1.0% to 1.5% exhibited hole mobilities of 700 cm 2 /V s to 900 cm 2 /V s.