  We propose a new method to derive certain higher order estimates in quantum
electrodynamics. Our method is particularly convenient in the application to
the non-local semi-relativistic models of quantum electrodynamics as it avoids
the use of iterated commutator expansions. We re-derive higher order estimates
obtained earlier by Fr\"ohlich, Griesemer, and Schlein and prove new estimates
for a non-local molecular no-pair operator.
