A theoretical investigation to find thermodynamically optimum design conditions of conduction-cooled Peltier current leads is performed. A Peltier current lead (PCL) is composed of a thermoelectric element (TE), a metallic lead and a high temperature superconductor (HTS) lead in the order of decreasing temperature. Mathematical expressions for the minimum heat flow per unit current crossing the TE-metal interface and the minimum heat flow per unit current from the metal lead to the joint of the metal and the HTS leads are obtained. It is shown that the temperature at the TE -metal interface possesses a unique optimal value that minimizes the heat flow to the joint and that this optimal value depends on the material properties of the TE and the metallic lead but not the joint temperature nor electric current. It is also shown that there exists a unique optimal value for the joint temperature between the metal and the HTS leads that minimizes the sum of the power dissipated by ohmic heating in the current leads and the refrigerator power consumed to cool the lead, for a given length of the HTS.