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The model reanalyses on the screening potential (SP) for the classical one-component plasmas, presented by Rosenfeld [preceding paper, Phys. Rev. E 52, 2000 (1995)] have been re-examined in light of the Monte Carlo (MC) simulation data currently available. With due consideration of statistical uncertainties in the MC data, it is shown that these approximation schemes individually may not corroborate some of the MC data. The assessed value (h2/Γ=0.00±0.01) [Ichimaru et al., Phys. Rev. E 50, 2977 (1994)] of the quartic coefficient in the short-range expansion of the SP is consistent with all the data obtained by the first-principles direct MC samplings of h2 and can reproduce MC values of the radial distribution function and SP uniformly for 10 ? Γ ? 160.