We have calculated relaxation times by means of a general iterative procedure when the electron-phonon interaction is included via three scattering mechanisms : the acoustic deformation potential, the piezoelectric of the acoustic branch, and longitudinal optical mode coupling (LO). Confinement of LO vibrations is taken into account by means of an appropriate Hamiltonian, and this leads to some selection rules for this interaction, which are carefully discussed. Screening of the electron-phonon interaction is considered. Mobility calculations are carried out in a size-quantum-limit (SQL) approximation. We have compared the effects on the screening contributions of the different scattering mechanisms and the confinement effects, produced by the use of different approximations for the electronic part, ranging from a self-consistent solution to an infinite barrier model.