i guess it depends on your instrument. My ESP, for instance, i can tune to just about anything without destroying playability...i did play it a whole step down for about 6 months, and that required heavy gauge strings and quite a truss rod adjustment, but it worked fine.
my fender jazz bass, however, doesn't work with me quite so much. even sudden shifts in the weather (i live in new england) cause the neck and action to go crazy...some days i'll wake up and almost every fret is buzzing. i have found that dropping to D during a show usually goes pretty smoothly, but anything beyond that would certainly require a whole new setup from scratch.
just experiment with different things and settings...you say that when you go down to dropped D-flat it sounds crappy...i say - FIX IT! find out what is wrong--too bassy, no definition etc-- and work it out so you can do it with ease. try adjusting amp settings, try different string gauges (maybe a little heavier on the E string??) IMO/IME, you should be able to tune any "normal" bass anywhere in the F-C range (half-step sharp to two whole steps flat) as long as you set it up according to how it responds to the change.
good luck
rock.