  We reconsider the Hung and Shuryak arguments in favour of searching for the
deconfinement phase transition in heavy ion collisions {\em downward} from the
nominal SPS energy, at $E_{lab} \approx 30 \ GeV/A$ where the fireball lifetime
is the longest one. Using the recent lattice QCD data and the mixed phase
model, we show that the deconfinement transition might occur at the bombarding
energies as low as $E_{lab}=3 - 5 \ GeV/A$. Attention is drawn to the study of
the mixed phase of nuclear matter in the collision energy range $E_{lab}= 2-10
\ GeV/A$.
