  We show that a triple-Regge parametrization of inclusive single diffraction
agrees with the data in the following two domains: (a) xi > 0.03 at all t, (b)
|t| > 1 GeV^2 at all xi. Since the triple-Regge parametrization fails when
applied to the full xi-t range of the total single-diffractive cross section,
we conclude that damping occurs only at low-xi and low-|t|. We give a (``toy'')
parametrization of the damping factor, D(xi), valid at low-|t|, which describes
the diffractive differential cross-section (dsig/dt) data at the ISR and
roughly accounts for the observed s-dependence of diffractive total
cross-section up to Tevatron energies. However, an effective damping factor
calculated for the CDF fitted function for dsig/dxidt at sqrt(s} = 1800 GeV and
|t| = 0.05 GeV^2, suggests that, at fixed-xi, damping increases as s increases.
  We conjecture that, in the regions where the triple-Regge formalism describes
the data and there is no evidence of damping, factorization is valid and the
Pomeron-flux-factor may be universal. With the assumption that the observed
damping is due to multi-Pomeron exchange, our results imply that the recent UA8
demonstration that the effective Pomeron trajectory flattens for |t| > 1 GeV$^2
is evidence for the onset of the perturbative 2-gluon pomeron. Our damping
results may also shed some light on the self-consistency of recent measurements
of hard-diffractive jet production cross sections in the UA8, CDF and ZEUS
experiments.
