(Degenerate Comparison Principle). Let $X$ be a compact Kähler manifold of complex dimension $n$, let $\gamma$ be a closed real $(1,1)$-current with continuous local potentials or a closed positive $(1,1)$-current with bounded local potentials, and consider $\varphi,\,\psi\in{\cal P}_{\gamma}\cap L^{\infty}(X)$. Then