Another good rebel strategy is to look for planets that support the alliance but happen to be Imperial controlled due to the presence of Imperial troops. There is always at least one of these situations. You can tell because it's green, the Imperial color, but the star is bright, meaning the population supports you. Anyway, once you found it, have your characters sabotage the troops stationed there until all of them are destroyed. When no Imperial troops remain, the planet will switch sides to your control, and many others in the system may be inspired to do so too.