Nine quaternary (Al,Ga,In)-(P,As,Sb) semiconductor compounds lattice matched to InP are investigated theoretically. Direct bandgap, refractive index at 1.55 µm wavelength, and thermal conductivity are calculated as a function of the composition. These material properties are important, e.g. in distributed Bragg reflectors of vertical-cavity lasers. The alloy systems AlGaAsSb, AlGaPSb and GaInPSb are found to promise better performance of those mirrors than the common InGaAsP system.