+1 to purging.
Actually, I purge 3 times. Once with plain tap water to rinse them off let them sit in the water for about 20 mins, then drain the water, add fresh and also add some semolina (corn meal) to the water. Not a lot, like maybe a tablespoon. The mussles (live ones) mistake the semolina for sand and purge out the sand they have in their mouths and suck in the semolina. Let them soak in that for another 20 mins then drain and rinse them off. Soak in ice water for another 20 mins.