  The renormalization algorithm based on regularization methods with two
regulators is analyzed by means of explicit computations. We show in particular
that regularization by higher covariant derivative terms can be complemented
with dimensional regularization to obtain a consistent renormalized
4-dimensional Yang-Mills theory at the one-loop level. This shows that hybrid
regularization methods can be applied not only to finite theories, like \eg\
Chern-Simons, but also to divergent theories.
