Zacam, here is what neb2 command documentation says:
neb2_break_alpha: Alpha value (0.0 to 1.0) at which faded polygons are not drawn. Higher values generally equals higher framerate, with more visual cloud popping.
Using neb2_break_alpha 0.0 seems to get rid of popping nicely for distant poofs.
neb2_break_off: How many pixels offscreen (left, right, top, bottom) when a cloud poof becomes fully transparent. Lower values cause quicker fading.
I chose arbitrarily large value of 8192 pixels offscreen (neb2_break_off 8192) to make sure that the close poofs don't pop out.
I didn't include the eff files for animated poofs because they didn't work, so there was really no point.
Concerning the PCX backgrounds, those are really weird. As far as I can tell, the image is not used at all (you can paint it black, or really anything, that's why I left the ugly fractal pattern), it is only used to set the color of the fog and the background, and even that in some weird way - it seems to me that the game takes the average of colors in the color palette.
Object pop-out seems to happen once the object is at 100% fog distance. Makes sense, as then you don't have to draw it anymore, since it's the same color as the background.
Unfortunatelly, once you start using skyboxes for backgrounds, you get object pop-in, because you don't have homogenous color background anymore (and skyboxes are additively blended on top of the fog color as far as I can see - that's why my skybox textures are so dark and subtle)
Also, as I've written before, explosions and things like that are not affected by fog, which breaks the effect. See images - the arrows point out explosions caused by asteroids hitting the Aquitaine beyond 100% fog, yet they are at 100% opacity. It would be nice to get that fixed.
Final note, I've included the objecttypes.tbl, because various objects had various fog distance settings, which makes no sense. I've set them all to the same number (max distance 500m), which can be changed in FRED with fog multiplier on per mission basis.
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