Conduction-cooled Peltier current leads (PCLs) are optimized in a superconducting magnetic system. Optimum geometric factors, viz. the ratio of length to cross-sectional area, of both the copper lead and thermoelectric element, are simultaneously found to minimize the heat leak per PCL. A rigorous thermodynamic temperature-entropy (T-s) diagram is constructed. The heat leak as well as the total input power of both PCLs and conventional all-copper leads can be easily identified from the rectangular areas on the simple 2-D T s plane. (C) 2002 Published by Elsevier Science Ltd.