We present an analytical framework for the performance evaluation of laser satellite uplinks over the major probabilistic impairments, i.e., atmospheric turbulence and beam wander. Specifically, we consider a ground-station-to-space laser uplink with a Gaussian beam wave model, and we focus on the particular regime assuming untracked beams where beam wandering takes place. In that regime, the modulated gamma-gamma distribution has been proposed as an effective irradiance model to characterize the combined effect of turbulence and beam wander. First we provide a closed-form expression of the probability density function and deduce the fundamental statistics of the new model. Then we evaluate the performance of the laser system assuming coherent detection for several modulation schemes. An appropriate set of numerical results is presented to verify the accuracy of the derived expressions.