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Pre-filtering for reducing ringing artifacts of Neatimage.

Neatimage has terrible ringing artifacts on darkest pixels around edges, but masked Greycstoration helps to reduce it if it applied before Neatimage

Apply Greycstoration set -p 0.2 -a 0.9 \(>ヮ<) on a dupe layer, then add a mask from grayscale of a background with inversion, then lower gamma at 0.1 (or 0.05 might be better, but PS require 2 pass leveling in this case)
it strongly smooth out only darkest pixels.

Just a info because of my laziness