Uncertainties in the neutron data and correlations between them—covariances—are necessary both for estimating the errors of neutronic characteristics of reactors and shielding and for reducing these errors to an acceptable level by adjusting them on the basis of the analysis of the results of macro experiments. Up-to-date information on the uncertainties of neutron data is contained in three relatively independent libraries of evaluated neutron data: American ENDF/B-VII, Japanese JENDL-4.0, and Russian BROND-3.1. In this study, the covariance data from these libraries for the most studied fuel material—uranium-235— are compared among themselves and with the spread of the evaluated cross sections recommended in these libraries. It was found that, in the fast neutron region, the uncertainties attributed to the important characteristics such as the number of secondary fission neutrons and the fission cross section are comparable in their magnitudes with the spread of the evaluated values of these characteristics. Since the evaluations of neutron data in all the libraries are based on nearly the same set of experimental results, only differently averaged, this is evidence that the uncertainties assigned to them are too optimistic. It was also revealed that, in all the considered data, the balance of dispersions attributed to the total cross section and to its components—partial cross sections—is roughly disturbed. A method for data correction which eliminates the noted inconsistency is proposed. The revision concerns the uncertainties of the components of the scattering cross section—elastic, inelastic, the reaction ( n , 2 n )— and leads to a decrease in the errors attributed to the cross sections of these reactions. The proposed technique can be used to correct the covariance data for other reactor materials.