Yeah, Peregrine has the right idea. Items in real life that are "white" are rarely just pure white -- whether it's white wings, cat, sports car, etc. An item will actually look "more white" if you use off-whites, slightly greys, little-bit blues, and only pure white sparingly, to bring out the punch.
On these wings, for example, if I just painted them a white block, there would be a little (natural) shadow, but the wings would look more dull, even though they would, when photographed, have a color average closer to pure white: