The exchange narrowing of the J band of certain dye monomers upon aggregation in solution has been known since the 1930s. Here, we analyze the theoretical explanations put forward to account for these narrow absorption bands. Although the theories range from models of identical monomers interacting with vibrations to the opposite of rigid monomers with statistically distributed electronic site energies, all approaches exhibit exchange narrowing. However, we show that the origins of the narrowing are different. A unified theory incorporating the two approaches is presented in which features of both narrowing mechanisms are evident.