We investigate the extent to which "interaction-free" measurements perturb
the state of quantum systems. We show that the absence of energy exchange d
uring the measurement is not a sufficient criterion to preserve that state,
as the quantum system is subject to measurement-dependent decoherence. Whi
le it is possible in general to design interaction-free measurement schemes
that do preserve that state, the requirement of quantum coherence preserva
tion rapidly leads to a very low efficiency. Our results, which have a simp
le interpretation in terms of "which-way" arguments, open up the way to nov
el quantum nondemolition techniques.