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The results produced by a variety of currently available pointwise Monte Carlo neutron transport codes for the relatively simple problem of modeling a fast source of neutrons slowing down and thermalizing in water are compared. Initial comparisons showed rather large differences in the calculated flux: up to 80% differences. By working together to improve the results, iterations were done by (a) ensuring that all codes were using the same data, (b) improving the models used by the codes, and (c) correcting errors in the codes--no code is perfect. Even after a number of iterations, we still found differences, demonstrating that our Monte Carlo and supporting codes are far from perfect. In particular, we found that the often overlooked nuclear data-processing codes can be the weakest link in our systems of codes. The results presented here represent today's state of the art in the sense that all of the Monte Carlo codes are modern, widely available, and used codes. They all can use the most up-to-date nuclear data, and the results are recent; these are the results that current users of these codes should expect to obtain from them. As such, the accuracy and limitations of the codes presented here should serve as guidelines to code users in interpreting their results for similar problems. Results for the improved thermal scattering model now available, using advanced versions of N JOY-99.259, TRIPOLI-4.5, and MCNPX-2.6.f Beta, are presented. For comparisons among experimentally measured water cross sections and the unique JEFF-3.1 and ENDF/B- VII thermal scattering law, S(α, β) data are exemplified. [ABSTRACT FROM AUTHOR]