Compound parabolic concentrator (CPC) type collectors have been viewed as the optimal design for totally stationary concentrators. However the CPC is ideal only for uniform incident solar Bur averaged over the energy collection period. The actual yearly-averaged incident flux map turns out to be highly non-uniform, as a function of projected incidence angle, which implies that concentration can be increased markedly if optical collection efficiency is compromised. The question then becomes: what concentrator angular acceptance function is best matched to nature＇s radiation flux input, and how much energy can such a concentrator deliver? The recently-invented tailored edge-ray concentrator (TERC) approach could be used to determine optimal reflector contours, given the optimal acceptance angle function. We demonstrate that totally stationary TERCs can have around three times the geometric concentration of corresponding optimized stationary CPCs, with greater energy delivery per absorber area, in particular for applications that are currently being considered for stationary evacuated concentrators with the latest low-emissivity selective coatings, e.g. solar-driven double-stage absorption chillers (at around 170 degrees C) and solar thermal power generation (at around 250 degrees C).