  A recent paper [M. Seevinck and J. Uffink, Phys. Rev. A 65, 012107 (2002)]
presented a bound for the three-qubit Mermin inequality such that the violation
of this bound indicates genuine three-qubit entanglement. We show that this
bound can be improved for a specific choice of observables. In particular, if
spin observables corresponding to orthogonal directions are measured at the
qubits (e.g., X and Y spin coordinates) then the bound is the same as the bound
for states with a local hidden variable model. As a consequence, it can
straightforwardly be shown that in the experiment described by J.-W. Pan et al.
[Nature 403, 515 (2000)] genuine three-qubit entanglement was detected.
