  We consider a general version of the phenomenon of more nonlocality with less
entanglement, within the framework of the 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 conclusive
local distinguishability, the status for other cardinalities being already
known.
