I've just changed my strings (keeping the same brand and gauge at the moment) - up until now I've had at least two full winds before threading the string through and tightening, although with the thicker strings especially this led to quite a big bundle of winds on the posts by the time the strings were up to tension.
I also noticed the top E was doing a weird and annoying sitar-type thing when played open, but only when tuned to E. When tuned to D, it didn't happen.
It turned out that the number of winds was increasing the break angle over the nut, and actually reducing the downward pressure at the fretboard end of the slot, making it buzz against the bottom of the slot. At least, that's what I figure given that it didn't buzz when tuned to D; if the break angle was too shallow or the slot was worn/chipped, dropping the tuning would surely have made the buzz worse.
With fewer winds, this doesn't happen even when tuned up to E.
I've also got fewer winds on all the other strings, so smaller bundles of winds and shallower break angles over the nut. I couldn't swear to it, due to the obvious effect of new strings, but I do think they're actually ringing out better now.