There is a steady prejudice that the mirrors reflecting the light flux towards the source are necessary when the maximum possible one-stage concentration of solar radiation is required. The well-known parabolic dish collector is a most effective optical system among such mirrors. An alternative approach for creating the better-concentrating solar collectors is proposed and discussed in this paper. The optical design of the proposed type solar concentrator is based on the multi-imaging approach, which suggests shaping and superpositioning of multiple source images/caustics in the common focal zone by a set of parabolic rings or bands. Such a technical concept possesses the two main advantages: very high concentration level, which can reach half of the thermodynamical limit, and rear disposition of the focal zone relatively far away from the reflecting elements. These advantages allow to apply parabolic blind-reflecting concentrators as a more promising solar optics for Stirling or photovoltaic power systems, as well as for various "immediate" thermal technologies and solar architecture of small individual cottages and social buildings.