If the spindle is empty, it could be that your hook is not set to allow the spindle to spin without wobbling. There's a great website on straightening the hook here.Basically, the idea is that the yarn you are spinning needs to be in a vertical line with the center of the spindle's shaft (top or bottom whorl) to stop the spindle from wobbling. Yes, this means that half-hitched bottom whorl spindles tend to have a natural wobble. But, if you spin them really fast, the wobble is minimized.
The thickness of the yarn and the thickness of the metal of the hook can also contribute to wobble -- what was a straight line with fine yarn, for instance, may become crooked when spinning on the same spindle with a thicker yarn.
If your spindle already has wool on it, then the wobble may be coming from uneven-ness in winding the cop. You want to wind on as evenly as you can -- be consistent in your wind-on style. This takes practice and trying wind-ons (the bee-hive style, the foot-ball style, take your pick) to find what consistently works for you. If it always wobbles once you reach a certain fullness, well, that's the spindle's way of telling you it is full! wind it off, enjoy the new yarn, and start with the next batch.
(expanded from a post to spindlers on 12/2001)
