A peaceful mind, accomplished through the steps, had me sleeping like a baby. From the day I took step five, about 6-8 weeks in, I have had no trouble sleeping.
Incidentally, it is not a silly thing to say you don't like pills. I dislike them intensely. Might be a legacy from my time in treatment and the doctors around at that time, but they regarded things like sleeping pills as solid alcohol. In my time i the fellowship I have seen enough to convince me they may have been right.