  For lambda phi^4 problems, convergent perturbative series can be obtained by
cutting off the large field configurations. The modified series converge to
values exponentially close to the exact ones. For lambda larger than some
critical value, the method outperforms Pade approximants and Borel summations.
We discuss some aspects of the semi-classical methods used to calculate the
modified Feynman rules and estimate the error associated with the procedure. We
provide a simple numerical example where the procedure works despite the fact
that the Borel sum has singularities on the positive real axis.
