  We present an explicit solution to the Skorokhod embedding problem for
spectrally negative L\'evy processes. Given a process $X$ and a target measure
$\mu$ satisfying an explicit admissibility condition we define functions
$\f_\pm$ such that the stopping time $T = \inf\{t>0: X_t \in \{-\f_-(L_t),
\f_+(L_t)\}\}$ induces $X_T\sim \mu$. We also treat versions of $T$ which take
into account the sign of the excursion straddling time $t$. We prove that our
stopping times are minimal and we describe criteria under which they are
integrable. We compare our solution with the one proposed by Bertoin and Le Jan
(1992) and we compute explicitly their general quantities in our setup.
  Our method relies on some new explicit calculations relating scale functions
and the It\^o excursion measure of $X$. More precisely, we compute the joint
law of the maximum and minimum of an excursion away from 0 in terms of the
scale function.
