The current BHPs has a ambi safety. The thumbpieces are serrated steel. They are a bit too flat for me. Some people replace them with the Cylinder and Slide units. They have a pronounced shelf to perch a thumb on, but they stick out too far in my opinion. I knocked one off once, and the extended lever gouged my side (somewhat ample) while carrying in a inside-waistband holster.
For my current BHP, I sent one side of my ambi safety to Ted Yost. He built it up just enough so I can easily work it with my strong side thumb without worrying about it getting "wiped off" by accident. I left the other side alone.
