As a line-focus concentrating solar power (CSP) technology, linear Fresnel collectors have the potential to become a low-cost solution for electricity production and a variety of thermal energy applications. However, this technology often suffers from relatively low performance. A secondary reflector is a key component used to improve optical performance of a linear Fresnel collector. The shape of a secondary reflector is particularly critical in determining solar power captured by the absorber tube(s), and thus, the collector's optical performance. However, to the authors' knowledge, no well-established process existed to derive the optimal secondary shape prior to the development of a new adaptive method to optimize the secondary reflector shape. The new adaptive method does not assume any pre-defined analytical form; rather, it constitutes an optimum shape through an adaptive process by maximizing the energy collection onto the absorber tube. In this paper, the adaptive method is compared with popular secondary-reflector designs with respect to a collector's optical performance under various scenarios. For the first time, a comprehensive, in-depth comparison was conducted on all popular secondary designs for CSP applications. It is shown that the adaptive design exhibits the best optical performance.