  The Hardy test of nonlocality can be seen as a particular case of the Bell
tests based on the Clauser-Horne (CH) inequality. Here we stress this
connection when we analyze the relation between the CH-inequality violation,
its threshold detection efficiency, and the measurement settings adopted in the
test. It is well known that the threshold efficiencies decrease when one
considers partially entangled states and that the use of these states,
unfortunately, generates a reduction in the CH violation. Nevertheless, these
quantities are both dependent on the measurement settings considered, and in
this paper we show that there are measurement bases which allow for an optimal
situation in this trade-off relation. These bases are given as a generalization
of the Hardy measurement bases, and they will be relevant for future Bell tests
relying on pairs of entangled qubits.
