  We propose a new strategy for the experimental search of the QCD phase
transition in heavy ion collisions: One may tune collision energy around the
point where the lifetime of the fireball is expected to be longest. We
demonstrate that the hydrodynamic evolution of excited nuclear matter does
change dramatically as the initial energy density goes through the "softest
point" (where the pressure to energy density ratio reaches its minimum). For
our choice of equation of state, this corresponds to epsilon_i approx. = 1.5
GeV/fm^3 and collision energy E_lab/A approx. = 30 GeV (for Au+Au). Various
observables seem to show distinct changes near the softest point.
