Fission-fragment angular distributions were measured in the reaction of 4~ with 2~ near the fusion barrier. For nearly symmetric mass-/charge splits we find angular distributions symmetric around 0 = 90 degrees, however, with unusually large anisotropies. These develop gradually into forward-backward asymmetric distributions as one moves away from mass-/charge symmetry. This indicates that non-compound fission ('quasi-fission') competes with true fusion-fission. The relative contribution of quasi-fission to the total fission cross section is somewhere between 51 and 85%. In the framework of the extrapush model this is equivalent to an extra-extra push energy for compound-nucleus formation inside the true fission saddle point of 4 < Exx < 9 MeV in agreement with a recent empirical parametrization of fusion-barrier shifts based on fusion-fission cross sections. On the basis of cross sections for fusion-evaporation residues it had previously been concluded that fusion of 4~ with Pb isotopes occurs unhindered. Possible reasons for this apparent discrepancy are discussed. PACS: 25.70.Jj