  This paper explores the possibility that an exactly decoherent set of
histories may be constructed from an approximately decoherent set by small
distortions of the operators characterizing the histories. In particular, for
the case of histories of positions and momenta, this is achieved by doubling
the set of operators and then finding, amongst this enlarged set, new position
and momentum operators which commute, so decohere exactly, and which are
``close'' to the original operators. The enlarged, exactly decoherent, theory
has the same classical dynamics as the original one, and coincides with the
so-called deterministic quantum theories of the type recently studied by 't
Hooft. These results suggest that the comparison of standard and deterministic
quantum theories may provide an alternative method of characterizing emergent
classicality. A side-product is the surprising result that histories of momenta
in the quantum Brownian motion model (for the free particle in the
high-temperature limit) are exactly decoherent.
