Let $f$ and $g$ be concave functions such that $g(u)\leq f(u)$ for all $u\in N_{\mathbb{R}}$. Then ${\operatorname{dom}}(g)\subset{\operatorname{dom}}(f)$, $\operatorname{stab}(g)\supset\operatorname{stab}(f)$ and $g^{\vee}(x)\geq f^{\vee}(x)$ for all $x\in M_{\mathbb{R}}$.