In drop D tuning I prefer to drop the 6th string only to a D, leave the 1st string as it naturally is as a high E and play it open much of the time, especially if I am finger picking. That way I play a D chord as 000230 and a G chord as 020030. The D is really a D2 and the G is a G6. When possible I try to hammer on or choke the 4th string at the 3rd fret, giving me an ever so slightly sharped F note in the middle range. That F is a flatted 3rd relative to the D and a flatted 7th relative to the G. Enough music theory! Try it, and you may find the dissonace between that middle range F and the treble E really pleasing.

--- Steve