  We construct generally applicable small-loss rate expansions for the density
operator of an open system. Successive terms of those expansions yield
characteristic loss rates for dissipation processes. Three applications are
presented in order to give further insight into the context of those
expansions. The first application, of a two-level atom coupling to a bosonic
environment, shows the procedure and the advantage of the expansion, whereas
the second application that consists of a single mode field in a cavity with
linewidth $\kappa$ due to partial transmission through one mirror illustrates a
practical use of those expansions in quantum measurements, and the third one,
for an atom coupled to modes of a lossy cavity shows the another use of the
perturbative expansion.
