We introduce some inexact versions of the minimal residual smoothing (IMRS) technique to accelerate the standard multigrid convergence. These are modified versions of the minimal residual smoothing (MRS) technique introduced in an earlier paper . The IMRS acceleration schemes minimize the residual norm of the multigrid iterate in a subspace and reduce the cost of the standard MRS acceleration by about 40% for two dimensional problems and frequently achieve even faster convergence. Numerical experiments are employed to compare the performance of the exact and the inexact minimal residual smoothing schemes. Key words: Minimal residual smoothing, multigrid method, subspace minimization, conjugate gradienttype methods. AMS subject classifications: 65F10, 65N06. 1 Introduction In this paper, we concern ourself with efficient implementation of the minimal residual smoothing (MRS) schemes as general purpose acceleration techniques to speed up the convergence of the standard multigrid me..