In a multi-level laser the pump process involves several intermediate
levels. The details of the atomic excitation are often irrelevant so t
hat an effective heat bath description and a two-level-laser model are
applicable. The heat bath approximation may be too crude, however; it
does not predict phenomena such as intensity-noise squeezing and sub-
Poissonian field statistics. We show how, in the general situation, th
e multi-level description can still be reduced to a two-level descript
ion in terms of a non-Markovian master equation where a rate matrix, r
ather than a single rate, accounts for the excitation process. The res
ulting dependence of the excitation rates on the state of the laser fi
eld constitutes a correction to the standard laser model. We hold it r
esponsible for the dynamic noise reduction in multi-level lasers.