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We propose a new strategy for the experimental search of the QCD phasetransition in heavy ion collisions: One may tune collision energy around thepoint where the lifetime of the fireball is expected to be longest. Wedemonstrate that the hydrodynamic evolution of excited nuclear matter doeschange dramatically as the initial energy density goes through the "softestpoint" (where the pressure to energy density ratio reaches its minimum). Forour choice of equation of state, this corresponds to epsilon_i approx. = 1.5GeV/fm^3 and collision energy E_lab/A approx. = 30 GeV (for Au+Au). Variousobservables seem to show distinct changes near the softest point.Comment: 7 pages, 3 Postscript figures (tar compressed and uuencoded)  submitte

Hydrodynamics near the QCD Phase Transition: Looking for the Longest-Lived Fireball