A new experimental approach is introduced to investigate the relaxation of the nuclear deformation degrees of freedom. Highly excited fissioning systems with compact shapes and low angular momenta are produced in peripheral relativistic heavy-ion collisions. Both fission fragments are identified in atomic number. Fission cross sections and fission-fragment element distributions are determined as a function of the fissioning element. From the comparison of these new observables with a nuclear-reaction code a value for the transient time is deduced.