Having followed a number of trailers I noticed a lot of swaying on some, and have heard that towing a 5th wheel eliminates that sway. I have been looking at short 5th wheels and trailers in the 20-25 ...
True sway is, generally, an indication of a poor set-up. Could be a tongue that's too light, WD not set up correctly, too much weight for the tow vehicle, etc...
That said, drifting and our 'wiggling' might be perfectly normal. In 7 years of our current set-up, I've never once experienced sway. I might, however, drift a bit when passed by a semi or, as TurnThePage noted, wiggle my tail a bit to get a look behind me.