Proposals are made for improving current second-generation superhomogénéisation (SPH) methods in three different ways and to use them in heterogeneous and homogeneous diffusion procedures for reactor design and operating calculations. The first improvement consists of using a surface radial leakage model in the flux calculation to represent the macroscopic flux curvature in the assembly. The second improvement is accomplished by the introduction of the Selengut normalization in the SPH equivalence procedure replacing the flux-volume normalization currently used with second-generation methods. Finally, the buckling calculation is improved to better represent the target color-set. Second- and third-generation SPH techniques for heterogeneous or homogeneous diffusion procedures are now implemented as a unified algorithm in a lattice code. Two-group benchmarks are proposed to measure precisely the equivalence effectiveness and the improvement gained with third-generation methods.