The structural, electronic and vibrational properties of the ordered-vacancy compound CdIn2Te4 have been studied theoretically in three phases. They are the tetragonal I (4) over bar and I (4) over bar 2m phases, and a potential high-pressure Fd (3) over barm phase. We found that: (i) the I (4) over bar and I (4) over bar 2m phases were virtually identical in total energy; (ii) a high pressure phase transition from either tetragonal phase to the Fd (3) over barm phase was unlikely; and (iii) the tetragonal phases were semiconducting with a direct band gap, while the Fd (3) over barm phase was metallic. We calculated the Raman and IR modes for the I (4) over bar 2m phase and compared these with experimental values.