  For a complete metric space $M$, we prove that the finitely supported extreme
points of the unit ball of the Lipschitz-free space $\mathcal{F}(M)$ are
precisely the elementary molecules $(\delta(p)-\delta(q))/d(p,q)$ defined by
pairs of points $p,q$ in $M$ such that the triangle inequality
$d(p,q)<d(p,r)+d(q,r)$ is strict for any $r\in M$ different from $p$ and $q$.
To this end, we show that the class of Lipschitz-free spaces over closed
subsets of $M$ is closed under arbitrary intersections when $M$ has finite
diameter, and that this allows a natural definition of the support of elements
of $\mathcal{F}(M)$.
