  We consider parameters $\lambda$ for which $0$ is preperiodic under the map
$z\mapsto\lambda e^z$. Given $k$ and $l$, let $n(r)$ be the number of $\lambda$
satisfying $0<|\lambda|\leq r$ such that $0$ is mapped after $k$ iterations to
a periodic point of period $l$. We determine the asymptotic behavior of $n(r)$
as $r$ tends to $\infty$.
