  We introduce a new Hamiltonian model which interpolates between the
Jaynes-Cummings model and other types of such Hamiltonians. It works with two
interpolating parameters, rather than one as traditional. Taking advantage of
this greater degree of freedom, we can perform continuous interpolation between
the various types of these Hamiltonians. As applications we discuss a paradox
raised in literature and compare the time evolution of photon statistics
obtained in the various interpolating models. The role played by the average
excitation in these comparisons is also highlighted.
