I've definitely had plants damaged by neem before. Despite its supposed safety promoted by a thousand websites, the neem-solution seeps into the soil and damages the roots. This leads to a dilemma: either I spray the plant so lightly that I get minimum drippage, but then it's not completely covered and the aphids simply migrate to the uncovered parts or new growths, meaning it's a never-ending battle, or I spray it so heavily that I get them all but it inevitably ends up dripping into the soil. This is no good.

So I need some ideas. Which insecticides can be used against aphids on indoor plants but are actually harmless to sensitive succulent roots? I just don't want to have to worry about the roots at all.