A method is presented for the reduction of large sets of related uncertainty sources into strongly reduced representations which retain a suitable level of correlation information for use in many cases. The method provides a self-consistent means of determining whether a given analysis is sensitive to the loss of correlation information arising from the reduction procedure. The method is applied to the ATLAS Jet Energy Scale (JES) uncertainty, demonstrating that the set of 60+ independent sources can be reduced to form a representation constructed of 3 nuisance parameters. By forming a set of four such representations, it is shown that JES correlation information is retained or probed over the full parameter space to within an average of 1%. This procedure is expected to significantly reduce the computational requirements placed upon early ATLAS searches in the upcoming 2015 dataset while still providing sufficient performance and correlation structure to avoid changing the analysis results.