The inclusion of spectral cross-relaxation terms, which stem from stro
ng velocity-changing collisions, in the low-dimensional equations, whi
ch describe the dynamics of a single-mode, inhomogeneously broadened,
unidirectional ring laser, is shown to bring noticeable modifications
to the low-excitation self-pulsing phenomena which occur in bad-cavity
-configured high-gain lasers. The added cross-relaxation terms are sho
wn to reduce both the first and the second laser threshold. These term
s are also shown to modify the pulsation wave forms, and to greatly af
fect the hierarchy of the dynamical behavior.