(continuation) The vast cohomology computations of Carlson and Green-King (all 2-groups of order at most 128) rely on the computation of projective resolutions. In this point of view the Benson-Carlson construction is an effective way to compute a projective resolution of minimal complexity: Just compute a projective resolution up to the highest degree of the parameters and apply the construction.

@Mariano: 1. The cohomology of a cyclic group is known anyway. 2. In general, to apply the cited construction, you primarily need (information about) parameters. That's no big deal: For example, you can pick them from Chern classes of a faithful unitary representation. In particular no cohomology compuations are needed to obtain their degrees.