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In the existing studies of satellite laser communications, the variances in the azimuth and elevation axes of a swaying transmitter are usually assumed to be identical. In this correspondence, the analysis is extended to the general case in which these two variances are not the same. It is shown that the transmitter radial pointing error angle follows the Hoyt distribution. Furthermore, we prove that the instantaneous signal-to-noise ratio (SNR) follows the log-square-Hoyt distribution. Based on these results, we establish an optimization model to minimize the outage probability, subject to a specified transmitter power, by adjusting some system parameters such as the transmitter gain. A closed form of the solution is obtained and a set of representative curves are presented.