We present the results of an extensive numerical study on the formation and evolution of early distortions of the microwave background spectrum. The thermalization redshift, Z(therm), of arbitrary amounts of energy has been accurately determined. Simple formulae, yielding Z(therm) as a function of the baryon density and of the chemical potential are given. The process of relaxation to a stationary spectrum (Bose-Einstein like) is investigated in detail; several earlier conclusions are revised. An analytic formula which provides a very accurate description of the final stationary spectrum is presented and used to reassess the observational constraints on the chemical potential. We also give simple formulae, yielding, as a function of the baryon density and of the chemical potential, the wavelength at which the maximum distortion occurs and the amplitude of the distortion.
