We demonstrate that the band-gap energies Eg of CuSb(Se,Te)2 and CuBi(S,Se)2 can be optimized for high energy conversion in very thin photovoltaic devices, and that the alloys then exhibit excellent optical properties, especially for tellurium rich CuSb(Se1−xTex)2. This is explained by multivalley band structure with flat energy dispersions, mainly due to the localized character of the Sb/Bi p-like conduction band states. Still the effective electron mass is reasonable small: mc ≈ 0.25m0 for CuSbTe2. The absorption coefficient α(ω) for CuSb(Se1−xTex)2 is at ω = Eg + 1 eV as much as 5-7 times larger than α(ω) for traditional thin-film absorber materials. Auger recombination does limit the efficiency if the carrier concentration becomes too high, and this effect needs to be suppressed. However with high absorptivity, the alloys can be utilized for extremely thin inorganic solar cells with the maximum efficiency ηmax ≈ 25% even for film thicknesses d ≈ 50−150 nm, and the efficiency increases to ∼30% if the Auger effect is diminished.