  One approach to the calculation of cross sections for infrared-safe
observables in high energy collisions at next-to-leading order is to perform
all of the integrations, including the virtual loop integration, by Monte Carlo
numerical integration. In a previous paper, two of us have shown how one can
perform such a virtual loop integration numerically after first introducing a
Feynman parameter representation. In this paper, we perform the integration
directly, without introducing Feynman parameters, after suitably deforming the
integration contour. Our example is the N-photon scattering amplitude with a
massless electron loop. We report results for N = 6 and N = 8.
