Rinse shellfish under running water to remove loose sediment, discarding any with broken shells. (Healthy shellfish close their shells when firmly tapped.) Transfer shellfish to a large pot of cold salted water (like their natural environment). Refrigerate, stirring occasionally, for 30 minutes. Just before cooking, lift the shellfish out of the water by hand, so that the sediment remains at the bottom of the pot. Mussels sometimes have small, fibrous “beards,” which you should pinch off. Spoon out the delicious juices when serving. Any grit released during cooking will fall to the bottom of the cooking liquid, where it should stay.