  A popular model of decoherence based on the linear coupling to harmonic
oscillator heat baths is analized and shown to be inappropriate in the regime
where decoherence dominates over energy dissipation, called pure decoherence
regime. The similar mechanism essentially related to the energy conservation
implies that, on the contrary to the recent conjectures, chaotic environments
can be less efficient decoherers than regular ones. Finally, the elastic
scattering mechanism is advocated as the simplest source of pure decoherence.
