The study of environmentally induced superselection and of the process
of decoherence was originally motivated by the search for the emergen
ce of classical behavior out of the quantum substrate, in the macrosco
pic limit [W. H. Zurek, Phys. Rev. D 24, 1516 (1981); 26, 1862 (1982)]
. This limit, and other simplifying assumptions, have allowed the deri
vation of several simple results characterizing the onset of environme
ntally induced superselection; but these results are increasingly ofte
n regarded as a complete phenomenological characterization of decohere
nce in any regime. This is not necessarily the case: the examples pres
ented in this paper counteract this impression by violating several of
the simple general rules. This is relevant because decoherence is now
beginning to be tested experimentally [C. Monroe et al., Science 272,
1131 (1996); M. Brune et al., Phys. Rev. Lett. 77, 4887 (1996)], and
one may anticipate that, in at least some of the proposed applications
(e.g., quantum computers), only the basic principle of ''monitoring b
y the environment'' will survive. The phenomenology of decoherence may
turn out to be significantly different.