  An attempt is made to resolve certain incongruities within the Nambu -
Jona-Lasinio (NJL) and Polyakov loop extended NJL models (PNJL) which currently
are used to extract the thermodynamic characteristics of the quark-gluon
system. It is argued that the most attractive resolution of these incongruities
is the possibility to obtain the thermodynamic potential directly from the
corresponding extremum conditions (gap equations) by integrating them, an
integration constant being fixed in accordance with the Stefan-Boltzmann law.
The advantage of the approach is that the regulator is kept finite both in
divergent and finite valued integrals at finite temperature and chemical
potential. The Pauli-Villars regularization is used, although a standard 3D
sharp cutoff can be applied as well.
