  We consider a class of generalised single mode Dicke Hamiltonians with
arbitrary boson coupling in the pseudo-spin $x$-$z$ plane. We find exact
solutions in the thermodynamic, large-spin limit as a function of the coupling
angle, which allows us to continuously move between the simple dephasing and
the original Dicke Hamiltonians. Only in the latter case (orthogonal static and
fluctuating couplings), does the parity-symmetry induced quantum phase
transition occur.
