In a downlink scenario, the performance of laser satellite communications is limited due to atmospheric turbulence, which causes fluctuations in the intensity and the phase of the received signal, leading to an increase in bit error probability. In principle, a single-aperture phase-compensated receiver, based on adaptive optics, can overcome atmospheric limitations by adaptive tracking and correction of atmospherically induced aberrations. However, under strong turbulence situations, the effectiveness of traditional adaptive optics systems is severely compromised. We have developed an alternative intensity-based technique that corrects the wavefront by iteratively updating the phases of individual focal-plane speckles, which maximizes the power coupled into a single-mode fiber. Here, we present the proof of concept for this method. We show how this technique offers around 4 dB power gain with fewer than 60 power measurements under strong turbulence conditions. It delivers a good performance in different turbulent regimes, and it shows robustness against severe deterioration of the signal-to-noise ratio.