  The reflected process of a random walk or L\'evy process arises in many areas
of applied probability, and a question of particular interest is how the tail
of the distribution of the heights of the excursions away from zero behaves
asymptotically. The L\'evy analogue of this is the tail behaviour of the
characteristic measure of the height of an excursion. Apparently the only case
where this is known is when Cram\'er's condition hold. Here we establish the
asymptotic behaviour for a large class of L\'evy processes which have
exponential moments but do not satisfy Cram\'er's condition. Our proof also
applies in the Cram\'er case, and corrects a proof of this given in Doney and
Maller [5].
