  We show a sufficient criterion to determine if a planar set $\Omega$ is a
minimizer of the prescribed curvature functional among all of its subsets. As a
special case, we derive a sufficient criterion to determine if $\Omega$ is a
self-Cheeger set, i.e. if it minimizes the ratio $P(E)/|E|$ among all of its
subsets. Specifically, if a Jordan domain $\Omega$ possesses the interior disk
property of radius $|\Omega|/P(\Omega)$, then it is a self-Cheeger set; if it
possesses the strict interior disk property then it is a minimal Cheeger set,
i.e. the unique minimizer. As a side effect we provide a way to build
self-Cheeger sets.
