I think propranolol worked quite well for my past Lithium tremors. The first time I took Lithium, I took 1,200 mg, had horrible tremors, but wasn't taking propranolol yet. The second time (3 years later) I took 900 mg Lithium, was then taking propranolol, and barely noticed tremors.

As for anxiety...also helpful. I wouldn't say it fights it like a benzo, but as a supplemental anxiety fighter, it might better help do the trick. I was actually originally prescribed propranolol for tachycardia. For that, it also worked great. In many peoples' cases anxiety shows itself in the form of racing heart. If something calms that, often some anxiety is calmed.

The highest propranolol dose I ever took was 60 mg per day (20/20/20). For at least 10 years I took at least 40 mg daily (20 mg morn/20 mg evening). I don't recall even one solitary side effect, at those doses. Only did me good. I don't take it now only because it's not available in Czech Republic. My doctor had to switch me to metoprolol, which is also a helpful and friendly beta blocker. I don't count this in my psych med list, but rather as a physical issue med. Actually, it's hard to know how much my tachycardia has been from anxiety and/or mood elevation, and how much heart-related. I have mitral valve prolapse, but how much that was the cause, is unsure.