A theoretical framework is introduced that describes possible CPT-violating effects in the context of quantum electrodynamics. Experiments comparing the anomalous magnetic moments of the electron and the positron can place tight limits on CPT violation. The conventional figure of merit adopted in these experiments, involving the difference between the corresponding g factors, is shown to provide a misleading measure of the precision of CPT limits. We introduce an alternative figure of merit, comparable to one commonly used in CPT tests with neutral mesons. To measure it, a straightforward extension of current experimental procedures is proposed. With current technology, a CPT bound better than about 1 part in 1020 is attainable.