Gently rub the surface of your sweater with a pumice stone (yes, that thing that smoothes out rough heels). You might need to (carefully!) clip big pills with scissors, but the stone will detach the rest without harming the weave. Your sweater will look as good as new!
Thanks to Julie Edelman, author of The Accidental Housewife: How to Overcome Housekeeping Hysteria One Task at a Time (Ballantine), for help with this tip.
More help with your woolens…