I start removing hay and twigs (and grass and weeds and seeds and grain -- anything not-wool) on the raw wool; fresh fleeces get put on a skirting table (a large chicken-wire-covered frame resting on sawhorses) and shaken, so the looser hay and grass bits fall to the ground. All this foreign matter is generally called "vegetable matter" or VM by the sheep-literati.
Once I have it washed and dried, I'll pick out a handful at a time to open up and shake. The opening of the fibers helps the bits fall out. Seed heads and burrs are stickier though, I go after them one-by-one, picking them out. Usually in the evening with a sheet on the floor in front of me and a good movie in the player.
I keep on removing hay and weeds through out the carding process -- flicking the locks open or picking them with a picker, and more still fall out under the carder during carding.
I even keep picking out bits during spinning. Some of those little pesky things I'm sure still lurk in the yarn, but they are there to stay!
Commercial processors use chemicals to dissolve or crushing to grind the plant matter to bits, if they have explicit processes in place to remove them. Zeilinger's uses a crusher, and in my experience, having sent them very-VMy fleece, they did a great job!
posted by me on spindlers, 22mar07
