  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 one part in $10^{20}$ is attainable.
