A method enabling atomic velocity class selection by means of quantum
interference in the two-photon ionization of an atom through two quasi
resonant intermediate levels is studied. This method is compatible wit
h the Doppler cooling in optical molasses, and it is able to attain te
mperatures colder than the Doppler limit. The advantages and limitatio
ns of this method are discussed. We study the effect of the competitio
n with the Doppler cooling for temperatures lower than the Doppler lim
it, when the usual Doppler process heats the atoms rather than cools t
hem. The method is shown to be limited essentially by the loss of grou
nd-state atoms due to ionization. We also propose and study a ''source
'' scheme in which new atoms are continuously injected into the system
, leading to a nonvanishing stationary number of cold atoms. Finally,
we propose generalizations of the method that allows us to combine it
with Sisyphus-type mechanisms.