We consider the problem of(re)allocating the total endowment of an inf
initely divisible commodity among agents with single-peaked preference
s and individual endowments. We propose an extension of the so-called
uniform rule and show that it is the unique rule satisfying Pareto opt
imality, strategy-proofness, reversibility, and an equal-treatment con
dition. The resulting rule turns out to be peaks-only and individually
rational: the allocation assigned by the rule depends only on the pea
ks of the preferences, and no agent is worse off than at his individua
l endowment.