Phenomenological and physical aspects of the intrinsic tail spectra of the alkalihalides are studied referring to the new results on the intrinsic tail spectra of KBr and KI and to the temperature dependences of the lowest-energy Γ-exciton peak of the sodium- and potassium-halides. Systematically analysing the temperature dependence of the steepness parameter σs (T) of the Urbach rule for these halides, it is found that the frequency factor has the value nearly equal to the acoustic phonon energy at X or L of each host lattice and the steepness constant σs0 becomes larger in passing from fluoride to iodide. This halogen dependence of σs0 is discussed in terms of the hole band-mass of the Γ8-level.