We study the family of GaSb(001)-(4×3) reconstructions by ab initio density-functional theory. For each possible surface stoichiometry between the well-known Sb-poor α(4×3) and Sb-rich β(4×3) phases, we find thermodynamically stable reconstructions. Surface energies of (4×3) unit cells shifted relative to each other are computed for the thermodynamically stable phases. Especially, the energetic costs for unit-cell shifts along the [1[over ¯]10] direction with the length of one in-plane surface lattice constant are very low. In a comparative study, we show that this is similar to the β2(2×4) reconstructed GaAs(001) surface with a one-dimensional disorder along [1[over ¯]10], but different from the c(4×4) reconstruction. The diversity in surface stoichiometry and unit-cell shape allows us to explain the contradicting experimental results obtained by scanning tunneling microscopy and surface-diffraction techniques at finite substrate temperatures.