  We extend an $L^2$ energy gap result due independently to Min-Oo and Parker
(1982) for Yang-Mills connections on principal $G$-bundles, $P$, over closed,
connected, four-dimensional, oriented, smooth manifolds, $X$, from the case of
positive Riemannian metrics to the more general case of good Riemannian
metrics, including metrics that are generic and where the topologies of $P$ and
$X$ obey certain mild conditions and the compact Lie group, $G$, is
$\mathrm{SU}(2)$ or $\mathrm{SO}(3)$.
