My doctors had me on Lorazepam for anxiety for awhile, which helped. When that prescription ran out and I was feeling depressed as well as anxious, they prescribed Zoloft, which worked wonders for me depression-wise, but didn't help with anxiety. I never had any side effects with either of those, not drowsiness or anything.
When they had me on Doxepin, though, that was a whole 'nother story, heh. When I took that one I was fine throughout the day, but then night would hit and I'd be feeling suicidal--I'd get through that night and be fine the next day, then the next night the suicidal urges would hit again. Finally I spoke to my doctor about it and that's when they gave me the Zoloft.