Jellby, thank you for the tip about the "burn" overlay together with "levels". This could work out well for me. I have not worked much at all with Levels or Histogram. Must-conquer-fear, fear is the mind-killer.
I have been using a PSP dialog for "HSL" (Highlight, Midtone, Shadow) adjustment, where you use positive and negative settings to increase the strength of the - you guessed it - highlights, midtone, shadows. It works ok, but there is a lot of overlap between a dark-colored highlight and a light-colored midtone. And then using paintbrush and dodge-brush to bleach out lingering specks, but yes, that is tedious. Your way sounds simpler.
Thanks again. (I really need to try GIMP again, maybe I can learn to love it.

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