  We develop a non--perturbative method that yields analytical expressions for
the deflection angle of light in a general static and spherically symmetric
metric. It is an improvement on a method previously devised by the authors, and
provides a correct description of the photon sphere already to first order. We
also propose an alternative approach that provides general simpler formulas,
although with larger errors. We apply our technique to different metrics and
verify that the error is at most $0.5 %$ for {\sl all} regimes. We show that
our approximation is more accurate than others proposed earlier.
