  We show that the low energy behaviour of quite diverse impurity systems can
be described by a single renormalized Anderson model, with three parameters, an
effective level $\tilde\epsilon_d$, an effective hybridization $\tilde V$, and
a quasiparticle interaction $\tilde U$. The renormalized parameters are
calculated as a function of the bare parameters for a number of impurity
models, including those with coupling to phonons and a Falikov-Kimball
interaction term. In the model with a coupling to phonons we determine where
the interaction of the quasiparticles changes sign as a function of the
electron-phonon coupling. In the model with a Falikov-Kimball interaction we
show that to a good approximation the low energy behaviour corresponds to that
of a bare Anderson model with a shifted impurity level.
