  We derive bounds on the integrated density of states for a class of
Schr\"odinger operators with a random potential. The potential depends on a
sequence of random variables, not necessarily in a linear way. An example of
such a random Schr\"odinger operator is the breather model, as introduced by
Combes, Hislop and Mourre. For these models we show that the integrated density
of states near the bottom of the spectrum behaves according to the so called
Lifshitz asymptotics. This result can be used to prove Anderson localization in
certain energy/disorder regimes.
