Motivated by the increasing practical needs for simulation optimization of modern industrial systems, this paper proposes an efficient ranking and selection (R&S) procedure for selecting the best-simulated design from a finite set of alternatives in the presence of large stochastic noise. To obtain the correct selection under a limited simulation budget, the proposed procedure sequentially allocates the budget to minimize the evaluated uncertainty values of the selection through a two-step process based on the existing uncertainty evaluation (UE) procedure. This two-step process reduces the inefficiency of the underlying UE procedure while keeping its high robustness to noise, thereby achieving improved the efficiency for the proposed procedure in a noisy environment. This improved efficiency is demonstrated in comparative experiments with other R&S procedures on several benchmark problems. In particular, the experimental results of three practical optimization problems emphasize the necessity of the proposed procedure.