  The fact that the Environment Induced Decoherence approach offers no general
criterion to decide where to place the "cut" between system and environment has
been considered as a serious conceptual problem of the proposal. In this letter
we argue that this is actually a pseudo-problem, which is dissolved by the fact
that decoherence is a phenomenon relative to the relevant observables selected
by the measuring arrangement. We also show that, when the spin-bath model is
studied from this perspective, certain unexpected results are obtained, as that
of a system decohering in interaction with a very small environment.
