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We show that for two non-trivial lambda phi ^4 problems (the anharmonicoscillator and the Landau-Ginzburg hierarchical model), improved perturbativeseries can be obtained by cutting off the large field contributions. Themodified series converge to values exponentially close to the exact ones. Forlambda larger than some critical value, the method outperforms Pade'sapproximants and Borel summations. The method can also be used for series whichare not Borel summable such as the double-well potential series. We show thatsemi-classical methods can be used to calculate the modified Feynman rules,estimate the error and optimize the field cutoff.Comment: 4 pages, 7 figs., uses revtex; contains a discussion of the  double-wel

Simple Method to Make Asymptotic Series of Feynman Diagrams Converge