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Ongoing polar-direct-drive (PDD) implosions on the National Ignition Facility (NIF) [J. D. Lindl and E. I. Moses, Phys. Plasmas 18, 050901 (2011)] use existing NIF hardware, including indirect-drive phase plates. This limits the performance achievable in these implosions. Spot shapes are identified that significantly improve the uniformity of PDD NIF implosions; outer surface deviation is reduced by a factor of 7 at the end of the laser pulse and hot-spot distortion is reduced by a factor of 2 when the shell has converged by a factor of 10. As a result, the neutron yield increases by approximately a factor ofmore » 2. This set of laser spot shapes is a combination of circular and elliptical spots, along with elliptical spot shapes modulated by an additional higher-intensity ellipse offset from the center of the beam. This combination is motivated in this paper. It is also found that this improved implosion uniformity is obtained independent of the heat conduction model. This work indicates that significant improvement in performance can be obtained robustly with the proposed spot shapes.« less