  We consider simple-pole descriptions of soft elastic scattering for pp, pbar
p, pi+ p, pi- p, K+ p and K- p. We work at t and s small enough for
rescatterings to be neglected, and allow for the presence of a hard pomeron.
After building and discussing an exhaustive dataset, we show that simple poles
provide an excellent description of the data in the region - 0.5 GeV^2 < t <
-0.1 GeV^2, 6 GeV<sqrt(s)< 63 GeV. We show that new form factors have to be
used, and get information on the trajectories of the soft and hard pomerons.
