  Let $a\in (0,\infty)$. For a spectrally negative L\'evy process $X$ with
infinite variation paths the resolvent of the process killed on hitting the
two-point set $V=\{-a,a\}$ is identified. When further $X$ has no diffusion
component the Laplace transforms of the entrance laws of the excursion measures
of $X$ from $V$ are determined. This is then applied to establishing the
Laplace transform of the amount of time that elapses between the last visit of
$X$ to a given point $x$, before hitting some other point $y>x$, and the
hitting time of $y$. All the expressions are explicit and tractable in the
standard fluctuation quantities associated to $X$.
