[en] A pair of superconducting coupling magnets will be part of the Muon Ionization Cooling Experiment (MICE). They were designed and will be constructed by the Institute of Cryogenics and Superconductivity Technology, Harbin Institute of Technology, in collaboration with Lawrence Berkeley National Laboratory. The coupling magnet is to be cooled by using cryocoolers at 4.2K. In order to reduce the heat leak to the 4.2K cold mass from 300 K, a pair of current leads composed of conventional copper leads and high temperature superconductor (HTS) leads will be used to supply current to the magnet. This paper presents the optimization of the conventional conduction-cooled metal leads for the coupling magnet. Analyses on heat transfer down the leads using theoretical method and numerical simulation were carried out. The stray magnetic field around the HTS leads has been calculated and effects of the magnetic field on the performance of the HTS leads has also been analyzed