  We present a {\sl non--perturbative} method, called {\sl Parametric
Perturbation Theory} (PPT), which is alternative to the ordinary perturbation
theory. The method relies on a principle of simplicity for the observable
solutions, which are constrained to be linear in a certain (unphysical)
parameter. The perturbative expansion is carried out in this parameter and not
in the physical coupling (as in ordinary perturbation theory). We show that the
method is capable to resum the divergent perturbative series, to {\sl extract}
the leading asymptotic (strong coupling) behavior and {\sl predict} with high
accuracy the coefficients of the perturbative series.
