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We perform the optimal design of gas-cooled Peltier current leads (PCLs), such that their resulting heat leaking into superconducting magnets can be minimized. Superior to previous investigations, the effect of gas cooling on both the Cu lead and the thermoelectric element in a PCL is taken into consideration. Analytical temperature distribution is derived as well as the concerned heat leaking into superconducting magnets. Numerically iterative calculations are, therefore, avoided. Moreover, temperature-entropy diagrams are constructed to distinguish conventional all-Cu leads from PCLs with and without gas cooling. Both the heat leak and the input power of current leads can be easily identified from the areas subtended by the isotherms on the simple two-dimensional temperature-entropy plane.