Any effective field theory relies on power counting rules
that allow one to perform a systematic expansion of calculated
quantities in terms of some soft scales. However, a naive
power counting can be violated due to the presence of
various hard scales in a given scheme.
A typical example of such a scale is an ultraviolet regulator.
This issue is particularly challenging when the interaction is
nonperturbative. The power counting is expected
to be restored in the course of renormalization,
that is by redefining bare low-energy constants
in the effective Lagrangian.
Whether this procedure eventually leads to a self-consistent framework is not a priory obvious. We discuss various criteria of renormalizability
in application to nuclear chiral effective field theory and
provide several instructive counterexamples.