© 2022 Elsevier Inc.Within the refined Gribov–Zwanziger scenario for four-dimensional Yang–Mills theory in the Landau gauge, a gluon mass term is generated from the restriction of the gauge field configurations to the first Gribov region. Tissier and Wschebor have pointed out that adding a gluon mass term to the usual Faddeev–Popov action yields one-loop renormalization group improved gluon and ghost propagators which are in reasonable agreement with the lattice data even in the infrared regime. In this work, we extend their analysis to several alternative renormalization schemes and show how the renormalization scheme dependence can be used to achieve an almost perfect matching to the lattice data for the gluon and ghost propagators.