  We show that for two non-trivial lambda phi ^4 problems (the anharmonic
oscillator and the Landau-Ginzburg hierarchical model), improved perturbative
series can be obtained by cutting off the large field contributions. The
modified series converge to values exponentially close to the exact ones. For
lambda larger than some critical value, the method outperforms Pade's
approximants and Borel summations. The method can also be used for series which
are not Borel summable such as the double-well potential series. We show that
semi-classical methods can be used to calculate the modified Feynman rules,
estimate the error and optimize the field cutoff.
