  We describe a non-minimal higher-derivative extension of Einstein-Maxwell
theory in which electrically-charged black holes and point charges have
globally regular gravitational and electromagnetic fields. We provide an exact
static spherically symmetric solution of this theory that reduces to the
Reissner-Nordstr\"om one at weak coupling, but in which the singularity at
$r=0$ is regularized for arbitrary mass and (non-vanishing) charge. We discuss
the properties of these solutions and comment on the physical significance of
our results.
