Is there a way to "clip" or "clamp" the height of a normal, so that bumps go to a certain height and then abruptly flatten, as if chopped off? The pic may explain better.

Cycles. . . . . .

I don't want smaller bumps that are still basically bubble-shaped... I could get that by just decreasing the strength of the normal in my normal map node. 

What I want is for the bumps to come up from the surface at a certain strength, and then get abruptly clipped/clamped so that they're limited in how far they rise above the surface.

I thought of trying to use a color ramp or contrast node to limit the brightest and darkest parts of the image, to clip it that way, but it doesn't work. The normal map is one of those proper purple-colored things and not easily edited in photoshop. I tried playing with height and distance settings in a bump map, but that just seems to make shorter bubbles, not "cropped" bubbles.
Pass the bump height through a Math > Minimum node. Set the empty value to your desired clamp height.





0.5 Clip





0.75 Clip





No Clipping