We study the role that disorder plays in shaping the functional form of the optical absorption spectra of amorphous semiconductors. We find, for hydrogenated amorphous silicon, amorphous germanium, amorphous gallium arsenide, and amorphous indium phosphide, that, while the breadth of the absorption tail is a strong function of disorder, the mean energy gap is insensitive to the amount of disorder. As the disorder is decreased, the optical absorption spectra associated with these amorphous semiconductors approach well defined disorderless limits, the energy gaps associated with these limits being greater than the corresponding crystalline gaps. The physical implications of these results are discussed. ©1998 American Institute of Physics.