  The study of environmentally induced superselection and of the process of
decoherence was originally motivated by the search for the emergence of
classical behavior out of the quantum substrate, in the macroscopic limit. This
limit, and other simplifying assumptions, have allowed the derivation of
several simple results characterizing the onset of environmentally induced
superselection; but these results are increasingly often regarded as a complete
phenomenological characterization of decoherence in any regime. This is not
necessarily the case: The examples presented in this paper counteract this
impression by violating several of the simple ``rules of thumb''. This is
relevant because decoherence is now beginning to be tested experimentally, and
one may anticipate that, in at least some of the proposed applications (e.g.,
quantum computers), only the basic principle of ``monitoring by the
environment'' will survive. The phenomenology of decoherence may turn out to be
significantly different.
