A simple coupled-cluster-type approximation is introduced, which generalizes in momentum ([ital k]) space a method recently presented in the literature for real space, and tested on the exactly solvable [ital XXZ] anisotropic quantum antiferromagnetic spin-1/2 chain. We implement our approximation in [ital k] space on the fermionized version of this model, and obtain improved results, with remarkable quantitative and qualitative features.