Let p = 0 or a prime. We characterize all finite quasi-simple groups for which the degrees of all irreducible p-Brauer characters are powers of a prime s. It turns out that this happens only for p = s = 2. As a consequence we have: If G is any finite group with the above condition on character degrees and p ≠ 2 or s ≠ 2 then G is solvable.