  We characterise the Banach spaces $X$ which are $L_1$-predual as those for
which every Lipschitz compact mapping $f:N\longrightarrow X$ admits, for every
$\varepsilon>0$ and every $M$ containing $N$, a Lipschitz (compact) extension
$F:M\longrightarrow X$ so that $\Vert F\Vert\leq (1+\varepsilon)\Vert f\Vert$.
Some consequences are derived about $L_1$-preduals and about Lipschitz-free
spaces.
