An unusually orderly excited state of a degenerate resonant molecular system occurs when all the resonant molecules are polarized in the same phase. The largest obtainable optical polarization of the medium is obtained under such conditions. Here we describe a technique by which such a maximally orderly excited state may be approached. Adiabatic fast half‐passage is used. Neither a tunable laser nor a tunable resonant medium is required, and disorder is not introduced by local intensity variations or degeneracy of the resonant levels. Nearly complete polarization of the available molecules has been measured by means of a phase‐switching technique.