Curlicues in your handspinning may occur in a variety of ways.
If it's a corkscrewing of the singles, then the likely culprit is too much twist. On a wheel, try backing off on pedaling - slow down pedaling but draft at the same rate. On a spindle, put less twist in for a given length of yarn -- twirl the spindle more slowly.
If it's little corkscrews of one single hanging off the side of the other single in the plying, that's a matter of tensioning the singles as you ply. If your lazy kate doesn't have a tensioner, feed the yarn through your fingers and be ready to stop the moment you feel one of these curled-up bits hit your fingers.
When I'm spinning fine, I get at least one curly-cue like this in the finished yarn (darn it!) -- so I snip it at its point, un-ply that section of yarn (twist a 4" length to unply it) then let it ply/twist back up, incorporating the two ends of the now-snipped curly-cue.
(posted by me on spindlers, 3/10/07)