This paper focuses on optical links from ground to a geostationary satellite, using adaptive optics to pre-compensate the wave-front of the uplink beam. We present the numerical prediction of the irradiance statistics at the satellite. Uplink beam diameters, as well as the turbulence strength in the boundary layer and in the tropopause are varied. Results show, that the choice of uplink beam diameter significantly affects the fading statistics, in particular the shape of the probability density function. In a realistic worst case (30° elevation, day-time turbulence, sea level), the optimum beam diameter, showing minimum irradiance fluctuation at the target, is around 20 cm. In that case, the probability of fades larger than 6 dB (with respect to the diffraction limit) is approx. 10 -3 .A breadboard of such a closed-loop adaptive-optics pre-compensation system has been implemented. It comprises a Shack-Hartmann wavefront sensor, two tip/tilt mirrors, a 140-element deformable mirror, a far-field propagation simulator, and two rotating turbulence phase screens (simulating tropopause and atmospheric boundary layer, respectively). The link geometry is representative of the intended application in an optical feeder link for geo-stationary satellites. Preliminary test results confirm the numerical predictions.