We report a comprehensive experimental and theoretical study of the structural and vibrational properties of α-CdIn₂Se₄ under compression. Angle-dispersive synchrotron X-ray diffraction and Raman spectroscopy evidence that this ordered-vacancy compound with pseudocubic structure undergoes a phase transition (7 GPa) toward a disordered rocksalt structure as observed in many other ordered-vacancy compounds. The equation of state and the pressure dependence of the Raman-active modes of this semiconductor have been determined and compared both to ab initio total energy and lattice dynamics calculations and to related compounds. Interestingly, on decreasing pressure, at ∼2 GPa, CdIn₂Se₄ transforms into a spinel structure which, according to calculations, is energetically competitive with the initial pseudocubic phase. The phase behavior of this compound under compression and the structural and compressibility trends in AB₂Se₄ selenides are discussed. (Figure Presented).