The subgroup method is used to compute self-shielded cross sections defined over coarse energy groups in the resolved energy domain. The validity of the subgroup approach was extended beyond the unresolved energy domain by partially taking into account correlation effects between the slowing-down source with the collision probability terms of the transport equation. This approach enables us to obtain a pure subgroup solution of the self-shielding problem without relying on any form of equivalence in dilution. Specific improvements are presented on existing subgroup methods: an N-term rational approximation for the fuel-to-fuel collision probability, a new Padé deflation technique for computing probability tables, and the introduction of a superhomogenization correction. The absorption rates obtained after self-shielding are compared with exact values obtained using an elastic slowing-down calculation where each resonance is modeled individually in the resolved energy domain.