  In the naive form of most resummations we get into conflict with
order-by-order renormalization. We present a method that is capable to ensure
UV consistency of any resummations satisfying certain conditions. The method is
based on the observation that resummation is equivalent with a calculation in
an adequate perturbation scheme, followed by a renormalization scheme changing.
This framework works both in static and momentum-dependent cases. In particular
it is possible to establish finite infrared 2PI resummation.
