  Maximally predictive states, as defined in recent work by Zurek, Habib and
Paz, are studied for more elaborate environment models than a linear coupling.
An environment model which includes spatial correlations in the noise is
considered in the non-dissipative regime. The Caldeira-Leggett model is also
reconsidered in the context of an averaging procedure which produces a
completely positive form for the quantum master equation. In both cases, the
maximally predictive states for the harmonic oscillator are the coherent
states, which is the same result found by Zurek,Habib and Paz for the
Caldeira-Legget environment.
