I also use warm water and dawn dish soap in a basin (usually bathroom sink) of water. Swish around, rinse a few times to get out all the soap and wrap in a towel for a bit then lay flat to dry. I've done cross-stich for years and never had an issue with DMC dyes running when cleaning in this fashion. Might need to go with a heavier detergent on the stains if they don't come out the first time. I'd be careful with the heavier detergents on the yarn, however.