  By an omega_1 --tree we mean a tree of power omega_1 and height omega_1. We
call an omega_1 --tree a Jech--Kunen tree if it has kappa --many branches for
some kappa strictly between omega_1 and 2^{omega_1}. In this paper we construct
the models of CH plus 2^{omega_1}> omega_2, in which there are Jech--Kunen
trees and there are no Kurepa trees.
