  Let $\alpha$ be a big class on a compact K\"ahler manifold. We prove that a
decomposition $\alpha=\alpha_1+\alpha_2$ into the sum of a modified nef class
$\alpha_1$ and a pseudoeffective class $\alpha_2$ is the divisorial Zariski
decomposition of $\alpha$ if and only if
$\operatorname{vol}(\alpha)=\operatorname{vol}(\alpha_1)$. We deduce from this
result some properties of full mass currents.
