  We consider the optimal prediction problem of stopping a spectrally negative
L\'evy process as close as possible to a given distance $b \geq 0$ from its
ultimate supremum, under a squared error penalty function. Under some mild
conditions, the solution is fully and explicitly characterised in terms of
scale functions. We find that the solution has an interesting non-trivial
structure: if $b$ is larger than a certain threshold then it is optimal to stop
as soon as the difference between the running supremum and the position of the
process exceeds a certain level (less than $b$), while if $b$ is smaller than
this threshold then it is optimal to stop immediately (independent of the
running supremum and position of the process). We also present some examples.
