Fast-fission reactions in collisions of four heavy systems (well below the fusion extra-push energy threshold), for which Hinde and coworkers had measured the prescission neutron multiplicities, have been analysed in terms of the deterministic dynamic model of Feldmeier coupled to a time-dependent statistical cascade calculation. In order to reproduce the measured prescission multiplicities and the observed (nearly symmetric) mass divisions, the energy dissipation must be dramatically changed with regard to the standard one-body dissipation: In the entrance channel, in the process of forming a composite system, the energy dissipation must be reduced to at least half of the one-body dissipation strength (k(s)(in) less than or equal to 0.5), and in the exit channel (from a mononucleus shape to scission) it must be increased to about 10 times that value (k(s)(out) approximate to 10).