Various evidence indicates that the atmospheric compositions of white dwarfs may switch from hydrogen- to helium- dominated, and vice versa, over wide ranges of surface temperature (luminosity). This envelope evolution may be understood only by assuming that the hydrogen (DA) sequence retains only a tiny residual mass of hydrogen, many orders of magnitude less than that predicted by stellar evolution theory. A corresponding problem may exist for the helium envelopes of some hot stars with helium-rich atmospheres.