We present the results of several parametrizations to two different ensemble of data on pp total cross sections (<FONT FACE=Symbol>s<img SRC="http:/img/fbpe/bjp/v31n4/07eq01.gif" ></FONT>) at the highest center-of-mass energies (including cosmic-ray information). The results are statistically consistent with two distinct scenarios at high energies. From one ensemble the prediction for the LHC (<img SRC="http:/img/fbpe/bjp/v31n4/07eq02.gif"> = 14 TeV) is<FONT FACE=Symbol>s<img SRC="http:/img/fbpe/bjp/v31n4/07eq01.gif" ></FONT> = 113 ± 5 mb and from the other, <FONT FACE=Symbol>s<img SRC="http:/img/fbpe/bjp/v31n4/07eq01.gif"></FONT> = 140 ± 7 mb. From each parametrization, and making use of derivative analyticity relations (DAR), we determine rho(s) (ratio between the forward real and imaginary parts of the elastic scattering amplitude). A discussion on the optimization of the DAR in terms of a free parameter is also presented. In all cases good descriptions of the experimental data are obtained.
