Some aspects of the problem of implosion symmetry in inertial confinement fusion (ICF) are discussed, with particular reference given to heavy ion beam fusion. The physics relative to the ignition of a target imploded by a driving pressure with long wavelength (low-mode number Legendre modes) asymmetries are studied by means of 2-D simulations. A parametric study shows that the tolerable level of non-uniformity is a decreasing function of mode number with the actual values depending on the specific target features (such as convergence ratio and ignition margin). The isobaric-fuel model of gain is then used to show how symmetry constraints (which limit the convergence ratio and the `hohlraum` transfer efficiency) affect the fuel energy gain. By using a model of ion beam energy conversion to X-rays, the gain of a class of indirectly driven targets is also estimated as a function of the relevant beam parameters.