In these simulation studies an energy weighting method is applied to the signals of the CMS hadronic calorimeter readout with a longitudinal segmentation for a possible future upgrade. Tabulated weighting factors are used to compensate for the different response of hadronic and electromagnetic energy depositions of simulated pion showers in the hadronic calorimeter. The weighting improves the relative energy resolution: (sigma(E)/E)(2) = {[}((92.2 +/- 0.6)\%/root E)(2) +((6.5 +/- 0.1)\%)(2)] (before weighting), (sigma(E,weight)/E)(2) = {[}((85.4 +/- 0.5)\%/root E)(2) + ((4.4 +/- 0.1)\%(2)] (after weighting), where E in the square root has units of GeV.