We present near-ideal axisymmetric numerically optimized spline concentrators (OSCs) which outperform the compound parabolic concentrator (CPC). By perturbing the profile of the revolved CPC by a variable-offset spline defined in tangent-normal space, we show that ray rejection can be reduced to nearly half of that of the CPC, without increasing concentrator length. The resulting OSCs achieve acceptance efficiencies as high as 99.3% for an acceptance angle of 45°, the highest reported for any finite-length CPC-like light concentrator. A set of design curves is presented which can be used to generate near "best-form" OSCs for any acceptance angle in the range 10° to 45°.