Using a flat-topped profile for the incident beam, the power scintillation index for weak atmospheric turbulence is formulated and analytically evaluated. Through the use of the aperture averaging factor, the averaging effect of the finite receiver aperture on the intensity fluctuations for a flat-topped incident beam is examined. The influence of the order of flatness on the averaging is investigated. At large propagation lengths, increasing the flatness parameter decreases the power scintillations and it is possible to further reduce the scintillation by increasing the receiver aperture. Increasing the structure constant increases this effect. (C) 2013 Elsevier Ltd. All rights reserved.