Endoreversible Joule-Brayton cogeneration cycle has been optimized based on a new criterion, total useful energy-rate (including power output and useful heat output), and the efficiency at maximum total useful energy rate has also been determined. The effects of various cycle parameters on the maximum dimensionless total useful-energy rate and the efficiency at maximum total useful-energy rate have been assessed. Variations of dimensionless total useful-energy rate with respect to efficiency have also been analyzed. The reversible Joule-Brayton power cycle is a special case of the analyzed cycle. (c) 2007 Elsevier Ltd. All rights reserved.