Let be a prime ideal in a commutative noetherian ring R and denote by the residue field of the local ring. We prove that if an R-module M satisfies for some, then holds for all. This improves a result of Christensen, Iyengar and Marley by lowering the bound on n. We also improve existing results on Tor-rigidity. This progress is driven by the existence of minimal semi-flat-cotorsion replacements in the derived category as recently proved by Nakamura and Thompson.