Hi, Glynis: My endo told me to start cutting back on the beta blockers a bit, when I began to get groggy all the time. This, of course, was after RAI, but it would probably hold true on the anti-thyroid meds, too. If the thyroid hormone levels are coming down, then the heart/tremor symptoms will be abating, also, and you won’t need the beta blockers as much, and they’ll make you tired.