Magnetic Resonance Imaging (MRI) scans are contraindicated for many patients with medical implants. We establish the circumstances that cause, and the resistances required to ameliorate and to eliminate dangerous levels of MRI-induced heating that occur at the exposed, distal end of an electrical lead implanted in tissue. Simulated predictions are compared with measurements made at 128 MHz in a 3-Tesla MRI machine. A low resistance at kilohertz frequencies is sought by implant makers, in contrast with the high resistance demanded for safety. The practicality of presently-developed strategies to prevent tissue damage is brought into question. We examine the extent to which skin-depth and transmission-line properties can be manipulated to improve safety.