Estimated error bounds derived from polynomial calculations have been used to revise the truncation error estimates of published data on gamma-ray penetration in water. It is also shown that more efficient use of moment data is possible to obtain greater accuracy in specific penetration regions and to extend the accuracy of polynomial calculations to greater penetrations. The results also indicate that in addition to the asymptotic power law, data to perhaps 40 mean-free-paths may be needed to make accurate extrapolations to arbitrarily great penetrations.