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By an ${\omega }_1$- tree we mean a tree of power ${\omega }_1$ and height ${\omega }_1$. Under CH and $2^{{\omega }_1}>{\omega }_2$ we call an ${\omega }_1$-tree a Jech-Kunen tree if it has κ-many branches for some κ strictly between ${\omega }_1$ and $2^{{\omega }_1}$. In this paper we prove that, assuming the existence of one inaccessible cardinal, (1) it is consistent with CH plus $2^{{\omega }_1}>{\omega }_2$ that there exist Kurepa trees and there are no Jech-Kunen trees, which answers a question of [Ji2], (2) it is consistent with CH plus $2^{{\omega }_1}={\omega }_4$ that there only exist Kurepa trees with ${\omega }_3$-many branches, which answers another...