  I discuss functional renormalization group (fRG) schemes, which allow for
non-perturbative treatment of the self-energy effects and do not rely on the
one-particle irreducible functional. In particular, I consider Polchinski or
Wick-ordered schemes with amputation of full (instead of bare) Green functions,
as well as more general schemes, and eastablish their relation to the
`dynamical adjustment propagator' scheme by M. Salmhofer [Ann. der Phys. 16,
171 (2007)]. While in the Polchinski scheme the amputation of full (instead of
bare) Green functions improves treatment of the self-energy effects, the
structure of the corresponding equations is not suitable to treat
strong-coupling problems; it is not also evident, how the mean-field (MF)
solution of these problems is recovered in this scheme. For Wick ordered
scheme, excluding fully or partly tadpole diagrams one can obtain forms of fRG
hierarchy, which are suitable to treat strong-coupling problems. In particular,
I emphasize usefullness of the schemes, which are local in cutoff parameter,
and compare them to the one-particle irreducible approach.
