Gribov-Pomeranchuk Poles in Scattering Amplitudes

It is shown that the argument of Gribov and Pomeranchuk for the existence of fixed poles in the $J$ plane at "nonsense" values of $J$ goes through in the presence of cuts, even though their argument for an essential singularity then fails. Such poles have no effect on the asymptotic behavior but, in cases where the contribution of the third double-spectral function is large, they will invalidate both the Schwarz superconvergence relations and the presence of dips in the asymptotic region. A Regge trajectory will not choose sense or nonsense at a point where it passes through an integer of the wrong signature.