  We consider a general version of the phenomenon of more nonlocality with less
entanglement, within the framework of the unambiguous (i.e., conclusive)
quantum state discrimination problem under local quantum operations and
classical communication. We show that although the phenomenon was obtained
before for two qutrits, it can also be observed for two qubits, while still
being at the single-copy level. We establish that the phenomenon is
intrinsically connected to the concept of unextendible entangled bases, in the
two-qubit case. In the process, we demonstrate a hierarchy of nonlocality among
sets of two-qubit orthogonal pure states, where the "nonlocality" is in the
sense of a difference between global and local abilities of quantum state
discrimination. We present a complete characterization of two-qubit pure
orthogonal state sets of cardinality three with respect to their nonlocality in
terms of unambiguous local distinguishability, the status for other
cardinalities being already known. The results are potentially useful for
secure quantum communication technologies with an optimal amount of resources.
