Existing data for large-t pp elastic-scattering differential cross-sec
tions are energy-independent and behave as t(-8). This has been explai
ned in terms of triple-gluon exchange, or alternatively through triple
-singlet exchange. A discussion is given of the problems raised by eac
h of these explanations, and of the possibility that at RHIC or LHC en
ergies the exchange of three BFKL pomerons might result in a rapid ris
e with energy.