The propagation of tightly focused light beams is analyzed from the no
n-paraxial scalar theory for light beam propagation. In particular, we
show how to minimize the width of the focused beam, measured with the
second order moment width of the irradiance distribution, by appropri
ately selecting the beam profile and the beam divergence angle. The op
timum profile and divergence, and the minimum waist width obtained are
found. A quality factor for non-paraxial beams is then proposed and i
ts lowest value found. These results are, on one hand, compared with t
he paraxial ones, on the other, are shown to remain valid to a good de
gree of accuracy when polarization effects are taken into account.