The symmetry of implosion of the hotraum target that has been proposed by J. Meyer-ter-Vehn and the author is analysed in the case when the target is driven by a nonspherical ensemble of heavy ion beams. The ion beams, each with a final focus radius rbf ⩾ R (R is the target radius), are all assumed to irradiate the target at the same angle α0 and symmetrically with respect to the equatorial plane. Separate one dimensional (1-D) simulations for the pole and equator target sectors indicate that the l = 2 mode in the asymmetry of fuel implosion vanishes for α0 ≈ 36°. The l = 4 mode can also be eliminated by adjusting the ion current profile across each beam. It is conjectured that the higher asymmetry modes with l ⩾ 6 will be smoothed out by radiative symmetrization to ≲ 1%. A 1-D average (over the target latitude) energy gain of G = 57 is calculated