Résumé : We have studied the mass and energy distributions of fission fragments from the two reactions 12C + 204Pb and 48Ca + 168Er that lead to the same compound nucleus 216Ra*. Despite the fact that the excitation energy was around 40 MeV in both cases, the contribution from asymmetric fission in the first reaction is only around 1.5% but is about 30% in the second. This marked increase in the yield of asymmetric products is connected to the quasifission process, in which important shell effects become evident. The mass-energy distributions are interpreted in terms of an independent decay mode competing with the normal fusion-fission process and possibly leading to a significant suppression of the fusion cross section itself.