  We present a revisited version of the nonextensive QCD-based Nambu -
Jona-Lasinio (NJL) model describing the behavior of strongly interacting matter
proposed by us some time ago. As before, it is based on the nonextensive
generalization of the Boltzmann-Gibbs (BG) statistical mechanics used in the
NJL model to its nonextensive version based on Tsallis statistics, but this
time it fulfils the basic requirements of thermodynamical consistency.
Different ways in which this can be done, connected with different possible
choices of the form of the corresponding nonextensive entropies, are presented
and discussed in detail. The corresponding results are compared, discussed and
confronted with previous findings.
