In the literature, the notion of eikonalization is often used as synon
ymous of unitarization or, at least, as implying that unitarity is not
violated. This, to the very least, appears to be wishful thinking. We
discuss the properties of various types of eikonalization within a un
ified treatment. Linear trajectories with intercept larger than unity
(so popular nowadays) lead to small asymptotic violations of unitarity
even after eikonalization. Classes of eikonalizations in which the Od
deron could dominate over the Pomeron are given; even so the maximal O
dderon is still excluded by eikonalization.