The theory of a new methodology for quantifying and then reducing the uncertainties in the pressure vessel fluences (or fluxes) of a pressurized water reactor (PWR) is described. The theory involves combining the results of calculated and measured dosimetry integral experiments along with differential data used in the calculations, together with covariances, into a generalized linear least-squares adjustment code named LEPRICON. The procedure solves the translation problem necessitated by the use of ex situ PWR dosimetry, and its covariance reducing potential is further enhanced by simultaneously combining the PWR data with a data base consisting of the results of analysis of simpler benchmark experiments. Development of this data base and a demonstration of the uncertainty reduction with application to one of the benchmark experiments are also described. For the example chosen, covariances of the calculated fluxes were reduced by factors of between 4 and 8.