For lighting applications demanding high brightness, a new type of LED-based light source has been developed, the high lumen density (HLD) source (luminance > 2·109 cd/m2). The performance can be improved further, among other things by optimizing the concentrator used as extraction optics. For this optimization, much insight is obtained by ray-tracing simulations. The efficiency can be improved by more than 20% if a high-index concentrator could be used. Furthermore, it is possible to optimize the shape of the concentrator. For a low-index (n ≈ 1.5) concentrator, the light leakage can be reduced, but the gain in useful light is only marginal. For a high-index (n ≈ 1.8) concentrator, the gain in useful light amounts to a few percent.