Extending the parameter space of the three-dimensional (d=3) Ising model, we search for a regime of eliminated corrections to finite-size scaling. For that purpose, we consider a real-space renormalization group (RSRG) with respect to a couple of clusters simulated with the transfer-matrix (TM) method. Imposing a criterion of "scale invariance," we determine a location of the nontrivial RSRG fixed point. Subsequent large-scale TM simulation around the fixed point reveals eliminated corrections to finite-size scaling. As anticipated, such an elimination of corrections admits systematic finite-size-scaling analysis. We obtained the estimates for the critical indices as ν=0.6245 (28) and yh =2.4709 (73). As demonstrated, with the aid of the preliminary RSRG survey, the transfer-matrix simulation provides rather reliable information on criticality even for d=3, where the tractable system size is restricted severely. © 2006 The American Physical Society.