A recyclable transmission line (RTL) carries power from the pulsed-power driver to the fusion target in a z-pinch-driven inertial-confinement fusion energy (IFE) system. In order to minimize the driver voltage, the RTL inductance must be small, requiring a short, low-impedance, magnetically insulated transmission line (MITL). However, the large linear current density that flows in the electrodes at small radius near the load resistively heats the anode surface, leading to anode plasma formation and ion emission. If the impedance of the RTL is too small, large ion current losses can occur and large electron flow currents can be launched into the z-pinch load region. These problems are avoided by choosing the line impedance at the load end of the RTL to be well above the effective impedance of the imploding load. By gradually reducing the impedance along the line moving from the load to the driver, the RTL inductance can be controlled. But, if the impedance is varied too rapidly along the line, significant electron flow current losses can occur. The impact of these constraints on the RTL design of an IFE system is discussed and a compromise design with reasonable power coupling efficiency is established.