In some applications of compound parabolic concentrators (CPCs), the incidence angle of solar rays on the absorber is restricted and must be less than a specified value (theta(e)) for efficient energy conversion or transfer. For a flat receiver with a restricted incidence angle (RWARIA, in short), two ideal concentrators designed based on one-sided flat absorber can be employed for radiation concentration: one is the CPC without exit angle restriction (CPC-1), and another is the CPC with a restricted exit angle (CPC-2). In this work, the angular dependence of optical efficiency factor of both CPC-1 and CPC-2 for concentrating radiation on the RWARIA was derived, and a mathematical procedure to estimate daily radiation accepted by the RWARIA by using east-west oriented CPC-1 and CPC-2 was suggested based on the solar geometry and monthly horizontal radiation. Results by numerical calculations show that, for fixed full CPC-1 and CPC-2 with identical acceptance half-angle (theta(a)), the CPC-2 is slightly more efficient than CPC-1 for concentration radiation on the RWARIA except periods of about 30 days before and after both equinoxes; whereas for fixed truncated CPC-1 and CPC-2 with identical geometric concentration factor (C-t) and theta(a), the CPC-2 is always more efficient. Results also indicate that, for the case of the tilt-angle of the aperture of CPCs being yearly adjusted four times at three tilts, full CPC-2 is less but truncated CPC-2 is more efficient than CPC-1 for concentrating radiation. In practical applications, CPCs are usually truncated due to less efficient of top portion of a CPC reflector for radiation concentration and less reflector material use, therefore, the CPC-2 is more favorable and advisable for concentrating radiation on the RWARIA. (C) 2013 Elsevier Ltd. All rights reserved.