  We study the consequences of high-energy collider data on the best fits to
total, elastic, inelastic, and single-diffractive cross sections for $pp$ and
$p \bar{p}$ scattering using different unitarisation schemes. We find that the
data are well fitted both by eikonal and U-matrix schemes, but that diffractive
data prefer the U-matrix. Both schemes may be generalised by means of an
additional parameter; however, this yields only marginal improvements to the
fits. We provide estimates for $\rho$, the ratio of the real part to the
imaginary part of the elastic amplitude, for the different fits. We comment on
the effect of the different schemes on present and future cosmic ray data.
