Circular Polarizer Reducing Dynamic Range Example
Prepared 2005-04-27 by Bill Claff

Proof that, at least this situation, a circular polarizer reduces dynamic range; rather than simply darkening the image uniformly as a Neutral Density (ND) filter would do.
I believe this is a typical result.

Two shots, seconds apart; top without polarizer, bottom with polarizer.
(D70 with 18-70mm @18mm f/7.1 1/400s and 1/100s respectively)
Shown resized but otherwise unprocessed with Photoshop CS Luminosity histograms to the right of each image.
The histograms are highlighted to show the dynamic range used.
No polarizer uses levels 7 to 234; 228 levels.
With polarizer uses levels 6 to 216; 211 levels.
With polarizer uses about 1/3EV less dynamic range in this case.
(I examined the linear raw data, not shown, to compute this.)
Also note that the right hand side of the luminance is "better behaved" with the polarizer.