  We analyze four and five-point tree-level open string S-matrix amplitudes in
the Regge limit, exhibiting some basic features which indicate longitudinal
nonlocality, as suggested by light cone gauge calculations of string spreading.
Using wavepackets to localize the asymptotic states, we compute the peak
trajectories followed by the incoming and outgoing strings, determined by the
phases in the amplitudes. These trajectories trace back in all dimensions such
that the incoming strings deflect directly into corresponding outgoing ones, as
expected from a Reggeon analysis. Bremsstrahlung radiation at five points
emerges from the deflection point, corroborating this picture. An explicit
solution for the intermediate state produced at four points in the $s$-channel
exists, with endpoints precisely following the corresponding geometry and a
periodicity which matches the series of time delays predicted by the amplitude.
We find a nonzero peak impact parameter for this process, and show that it
admits an interpretation in terms of longitudinal-spreading induced string
joining, at the scale expected from light cone calculations, and does not
appear to admit a straightforward interpretation purely in terms of the
well-established transverse spreading. At five points, we exhibit a regime with
advanced emission of one of the deflected outgoing strings. This strongly
suggests early interaction induced by longitudinal nonlocality. In a companion
paper, we apply string spreading to horizon dynamics.
