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 $E_{lab}= 2-10 \ GeV/A$.