Make the dressing: In a small bowl, whisk together the oil, lemon juice, mustard, salt, pepper, and sugar. Whisk in the dill, and set aside.
In a shallow microwave-safe casserole large enough to hold the mussels in one layer, cook the mussels, covered, for 2 minutes on full power (650 to 700 watts), or until opened. Discard any that do not open. Remove the muss