A theoretical investigation for optimization of conduction-cooled Peltier current leads is undertaken. A Pottier current lead (PCL) is composed of a thermoelectric element (TE), a metallic lead and a high Tc superconductor (HTS) lead in the order of decreasing thermoelectric tempera ture. Mathematical expression for the minimum heat flow per unit current crossing the TE metal interface and that flowing 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 73 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 current leads and the refrigerator power consumed to cool the lead, for a given length of the HTS.