  We introduce a new observable for reading out a which-way detector in a
Young-type interferometer whose eigenstates either contain full which-way
information or none at all. We calculate the which-way knowledge K that can be
retrieved from this observable and find that K depends on the phase difference
\delta that the interfering object accumulates on its way from either slit to
the detector. In particular, it turns out that K(\delta) has an upper bound of
1, almost independent of the visibility V of the interference pattern generated
by the interfering object on a screen, which is in marked contrast to the
well-known inequality K^2 + V^2 <= 1 (cf. B.-G. Englert, Phys. Rev. Lett. 77,
2154 (1996)).
