I talked to a head chemist of a chemical company, and he said neem oil is really good for getting rid of bugs. The only thing with neem oil is that it doesn't last that long and you need to respray once the eggs have hatched. He also said that with most neem oils you need to add an adjuvant to break the surface tension of water. This is why people add soap when they spray. Regular dish soap is bad for the plants, but he told me that baby shampoo won't be harmful. I used this method yesturday night because he told me it is bad to spray during the day. I see very positive results today, and there are no more black dots underneath the leaves. To recap, the mixture I used was 1 tsp of baby shampoo, 2 tsp of neem oil, and a spray bottle (quart) of water. Hope this helps,

Peace,
rider