  We compare schemes for testing whether two parties share a two-qubit singlet
state. The first, standard, scheme tests Braunstein-Caves (or CHSH)
inequalities, comparing the correlations of local measurements drawn from a
fixed finite set against the quantum predictions for a singlet. The second,
alternative, scheme tests the correlations of local measurements, drawn
randomly from the set of those that are $\theta$-separated on the Bloch sphere,
against the quantum predictions. We formulate each scheme as a hypothesis test
and then evaluate the test power in a number of adversarial scenarios involving
an eavesdropper altering or replacing the singlet qubits. We find the `random
measurement' test to be superior in most natural scenarios.
