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

Optimally stopping at a given distance from the ultimate supremum of a spectrally negative L\'evy process