  It is very likely that hadronic scattering will enter a new regime at the
LHC, as the black-disk limit is reached. This will lead to a severe change in
the t dependence of the real part and of the slope of the elastic scattering
amplitude, and in turn this may bias the measurement of the total cross
section. We examine this issue, and suggest new strategies to test the
reliability of the total cross section measurements.
