  We show that for the lower branch of the quark condensate and values higher
than approximately $-(250 \, \mathrm{MeV})^3$ the chiral critical end-point in
the Nambu--Jona-Lasinio model does not occur in the phase diagram. By using
lattice motivated non-local quark interactions, we demonstrate that the
critical end-point can be recovered. We study this behavior for a range of
condensate values and find that the variation in the position of the critical
end-point is more pronounced as the condensate is increased.
