Self-Healing Power Systems (SHePS) have potential to greatly improve electric power system resiliency. Many SHePS concepts rely on high-speed networked communications, which increase costs and can limit self-assembly capability. Thus, SHePS concepts that rely only on local measurements can play an important role. One key challenge in SHePS using only local measurements is in detecting and mitigating thermal overloads of conductors without shedding all loads on the overloaded conductor. This paper proposes a new thermal overload mitigation technique, referred to as the “tapping” method, that involves patterned switching of line relays to modulate the voltage and recognition of that switching pattern by downstream load-control relays, which then disconnect minimum-priority loads to relieve the overload. The loads can be automatically reconnected after a set of criteria is met, again using only local measurements. The technique is described in detail and demonstrated in PSCAD simulation.