Accurate band structures of binary semiconductors AB (A = Al, Ga, In and B = P, As, Sb) and selected ternary III–V semiconductors were calculated using an all-electron screened exchange approach within the full potential linearized augmented plane-wave method. Fundamental band gaps and Γ–L and Γ–X separations in higher-lying conduction bands are predicted with an accuracy of a few tenths of 1 eV. Screened exchange also performs better than the local density approximation for calculating conduction-band effective masses. Highly n-doped InPAs materials with compositions near InP₀.₂As₀.₈ offer lower effective masses, greater optical band-gap shifts, and potentially higher electron mobility than n-doped InGaAs materials with comparable band gaps.