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We present a toy model of a generic five-dimensional warped geometry in which the 4D graviton is not fully localized on the brane. Studying the tensor sector of metric perturbation around this background, we find that its contribution to the effective gravitational potential is of 4D type (1/r) at the intermediate scales and that at the large scales it becomes 1/r 1+α, 0 < α ≤ 1 being a function of the parameters of the model (α = 1 corresponds to the asymptotically flat geometry). Large-distance behavior of the potential is therefore not necessarily five-dimensional. Our analysis applies also to the case of quasilocalized massless particles other than graviton. © 2004 The American Physical Society.