A multilayer reflector useable to reflect or transmit light over the visible wavelength range includes optically thick constituent layers. The optical thickness of the constituent layers through the thickness of the reflector defines a layer thickness profile. The layers are arranged so that the thickness profile has a tailored non-uniform distribution, such as a graded distribution or a randomized distribution. The layers desirably have an optical thickness in a range from about one to five or one to ten design wavelengths. The reflector can be a polarizer, reflecting only one normally incident polarization state, or a mirror, reflecting two normally incident orthogonal polarization states.