  The dynamics of a resonant, free-running ring laser, in the common case of a
fast relaxation of the atomic polarization, is unexpectedly highly singular. As
shown in [Phys. Rev. Research, {\bf 5}, 023059 (2023)], this is due to the
closeness to a pure Hamiltonian dynamics ruled by a nonlinear wave equation,
herein named Klein-Gordon-Toda model. In this paper, we derive a
quasi-Hamiltonian model which allows describing realistic systems. In
particular, we identify two nearly conserved, energy-like quantities, which
``naturally" exhibit an ultra-slow dynamics confirmed and highlighted by
numerical simulations. A minimal version of the quasi-Hamiltonian model is
finally derived, which does not only reproduce the laser thresholds, but also
helps understanding the origin of the nearly integrable character of the laser
dynamics.
