  We consider a particularly simple exactly solvable model for a qubit coupled
to sequentially nested environments. The purpose is to exemplify the coherence
conserving effect of a central system, that has been reported as a result of
increasing the coupling between near and far environment. The paradigmatic
example is the Jaynes-Cummings Hamiltonian, which we introduce into a
Kossakowski-Lindblad master equation using alternatively the lowering operator
of the oscillator or its number operator as Lindblad operators. The harmonic
oscillator is regarded as the near environment of the qubit, while effects of a
far environment are accounted for by the two options for the dissipative part
of the master equation. The exact solution allows us to cover the entire range
of coupling strength from the perturbative regime to strong coupling
analytically. The coherence conserving effect of the coupling to the far
environment is confirmed throughout.
