We analyze Self-Limited Additive Pulse Mode-locked (SLAPM) lasers. SLA
PM is APM in which the effective fast saturable absorption rolls over
to become fast saturable gain for the pulse peaks, providing an import
ant stabilizing mechanism. The pulses in a SLAPM laser tend to look Ga
ussian at the top but maintain exponential wings and have time-bandwid
th products larger than that of a sech(2)-shaped pulse. We compare a s
imple analytic theory with two discrete computer simulations of SLAPM
lasers. We show that despite large nonlinear phase shifts per pass in
the fiber (close to pi) and the lumped nature of the elements in the l
aser, the analytic model is applicable. Both the simulated pulse param
eters and shapes show good agreement with the theory.