Parabolic trough type solar power plants could reach higher efficiencies by using secondary reflectors, which increase the concentration of the solar irradiance onto the absorber tube. Recently, compact secondary concentrators have been proposed which are constructed according to the edge ray principle; they are composed of an involute part and an edge ray reflector with a form close to a straight line. Using these reflector forms as a starting point, we optimize numerically various secondary concentrators and investigate their performance by means of raytracing, taking into account reflectivity losses, shading and the effective solar angular distribution, i.e. the sunshape. We investigate the performance of secondary concentrators with the outer part approximated by a straight line. The entire characteristic curve of collection efficiency versus concentration was investigated, for both a pillbox sunshape and a Gaussian sunshape. It is found that the secondary reflector significantly improves the concentration and is essentially optimal in a wide class of shapes, even at efficiencies close to unity.