Kathleen Taylor's "Yarns to Dye For" has some interesting methods for dyeing variegated yarns. I tried one last night. It didn't turn out quite as expected!
The dye was an acid dye (for protein fibers) and was a mixed color--blue dye and yellow dye mixed to give a deep bluegreen.
The method: wind your yarn in a loose (oops. Mine wasn't loose!) ball and immerse in dye bath. Every few minutes, pull out a few yards of yarn.
The result: My handspun wool yarn is now a beautiful robin's egg blue. It has subtle shading, but no overall variegation. (The idea is that the end that is pulled out of the dye bath first is pale and the end that is pulled out last is very dark.) Also, the blue dye obviously struck first--I added some rovings after the yarn was out of the dye bath and they are more green.
An interesting note: one of the rovings I added was a natural brown. It successfully picked up dye, so I know it can be overdyed. Unfortunately, bluegreen dye on brown looks sickly...it's a very creepy, witchy color to me! The photo below is out of focus but you can see some of the blue in the brown. What you can't see is the green that is also there! Eww!
I think I'll keep that one and see if it doesn't find a use around Halloween time!