Recent controversy in the literature about the structure of water away from ambient conditions is manifested by significant differences between the site-site pair correlation functions of water as derived from neutron diffraction data and the same quantities obtained in computer simulations using an effective pairwise potential for,the intermolecular interactions. One possible explanation of the discrepancies between computer models of water and neutron diffraction results near the critical point is that they arise from uncertainties in the inelasticity correction, which is particularly large for light water. To test out this idea, a new method of obtaining the pair correlations is described. This new analysis method is applied both to the earlier neutron data on non-ambient water and on recently reported data for a range of densities at 573 K. For this newer data the incident neutron spectrum is derived from an ambient water moderator instead of the liquid methane (100 K) moderator of previous work, and this has the effect of altering the shape of the inelasticity distortion to the diffraction data. It is found that the resulting site-site correlation functions from different experiments are now closely consistent with one another, indicating that the inelasticity correction has been Successfully performed by this new analysis. It is also demonstrated that the new site-site correlation functions can be generated from three-dimensional distributions of water molecules. The previously reported discrepancies between simulation and neutron data are not as severe with this new analysis, but there remain systematic trends with density and temperature which apparently are not reproduced by computer simulation with empirical pair potentials.