A strong nonlinear pressure dependence of the optical absorption edge has been measured in defect chalcopyrites CdGa2Se4 and HgGa2Se4. The behavior is due to the nonlinear pressure dependence of the direct band-gap energy in these compounds as confirmed by ab initio calculations. Our calculations for CdGa2Se4, HgGa2Se4 and monoclinic β-Ga2Se3 provide evidence that the nonlinear pressure dependence of the direct band-gap energy is a general feature of adamantine ordered-vacancy compounds irrespective of their composition and crystalline structure. The nonlinear behavior is due to a conduction band anticrossing at the Γ point of the Brillouin zone caused by the presence of ordered vacancies in the unit cell of these tetrahedrally coordinated compounds.