Systems with a discrete rotational symmetry [Formula: see text] where [Formula: see text] that also have electromagnetic duality symmetry exhibit zero backscattering. The impact of breaking one of the two symmetries on the emerging backscattering has not yet been systematically studied. Here, we investigate the effect that perturbatively breaking each of the two symmetries has on the backscattering off individual objects and 2D arrays. We find that the backscattering off electromagnetically-small prisms increases with the parameters that determine the symmetry breaking, and that the increase of the backscattering due to the progressive breaking of one of the symmetries can be related to the other symmetry. Further exploration of the interplay between the two symmetries reveals that, in systems lacking enough rotational symmetry, the backscattering can be almost-entirely suppressed for a given linear polarization by deliberately breaking the duality symmetry. This duality breaking can be interpreted as an effective increase of the electromagnetic degree of rotational symmetry for that linear polarization.