By manipulating a set of ion beams upstream of a target, it is possible to arrange for a smoother deposition pattern, so as to achieve more uniform illumination of the target. A uniform energy deposition pattern is important for applications including ion-beam-driven high energy density physics and heavy-ion beam-driven inertial fusion energy ("heavy-ion fusion"). Here, we consider an approach to such smoothing that is based on rapidly "wobbling" each of the beams back and forth along a short arc-shaped path, via oscillating fields applied upstream of the final pulse compression. In this technique, uniformity is achieved in the time-averaged sense; this is sufficient provided the beam oscillation timescale is short relative to the hydrodynamic timescale of the target implosion. This work builds on two earlier concepts: elliptical beams applied to a distributed-radiator target [D. A. Callahan and M. Tabak, Phys. Plasmas 7, 2083 (2000)] and beams that are wobbled so as to trace a number of full rotations around a circular or elliptical path [R. C. Arnold et al., Nucl. Instrum. Methods 199, 557 (1982)]. Here, we describe the arc-based smoothing approach and compare it to results obtainable using an elliptical-beam prescription. In particular, we assess the potential of these approaches for minimization of azimuthal asymmetry, for the case of a ring of beams arranged on a cone. It is found that, for small numbers of beams on the ring, the arc-based smoothing approach offers superior uniformity. In contrast with the full-rotation approach, arc-based smoothing remains usable when the geometry precludes wobbling the beams around a full circle, e.g., for the X-target [E. Henestroza, B. G. Logan, and L. J. Perkins, Phys. Plasmas 18, 032702 (2011)] and some classes of distributed-radiator targets. V C 2012 American Institute of Physics. [http://dx.