Just for fun I went to Wal-Mart today at lunch and found all the different motion sickness remedies available. There was a generic brand that DID not list drowsiness as a side effect, but that makes me wonder how effective it is. I also found the less-drowsy and regular Dramamine. Even the less-drowsy Dramamine listed possible drowsiness as a side effect. There was also Bonine, which of course causes drowsiness, and some kind of drops that I hadn't heard of, but that also had the side effects.
As a first time cruiser who does get motion sickness, I'm going to carry along the less-drowsy Dramamine, and also see about the pressure point bracelets. I figure that the worst case scenario is that I'll have to pay a visit to the ship's doctor!