BP meds that have little side effects

I have mild cardiomyopathy and my doctor has me on 20mgs/day of Alltace. That is not enough to lower my BP. I was on 12mg of coreg twice a day and ALLtace, but the Coreg lowered my pulse into the forties. I put up with it for over a year. The problem is my exercise routine has given me a low resting heart rate so coreg doses at 6mgs or higher lowers it too much. Doses of Coreg below 6mgs. do lower my BP some, but it generally stays in the upper 120s and 130s. Are there any other BP meds out there that lower BP without messing with the pulse. Peferrably one without many side effects? My doctor hasn't put me on anything but Alltace after I tried both coreg and metoprolol. I'd like to ask him about alternatives.