this paper we concentrate on convergence estimates for miminum residual iteration applied to a linear system Ax = b, (so that A represents the preconditioned coefficient matrix if preconditioning is employed). In particular we generalise the results of [25] to establish rigorous convergence estimates for families of matrices which depend on an asymptotically small parameter ff (in applications ff is typically a positive power of the mesh size parameter h). These results prove the superiority of the minimum residual approach over the solution of normal equations for all except one very special type of symmetric and indefinite matrix. More background and an easy introduction to this problem can be found in [8], pp. 310-315