The phases of complex spin-dependent scattering amplitudes for elastic
processes NN, piN, pid, along with pp --> dpi+, are analyzed in vario
us frames of reference for spin quantization. When all available energ
ies and angles are compiled it is seen that the ''phase histograms'' f
or each reaction have remarkably simple properties in one choice of op
timal frame; the phases tend to be integer multiples of 90-degrees, wi
thin existing uncertainties. A two-component model for piN is presente
d that reproduces the striking pattern of phases and its generalizatio
n is discussed.