The thing I have found most effective against SHB is sunshine. SHB love shade, hate sun. I don't think brush around the hive means much at all. Within a few feet of the hive, ground clutter needs to be removed, but other than that, sun is your friend.
Just an update to this thread: Since this original post I have moved both my hives where they receive the maximum sunshine anywhere on my property. Roughly 40 minutes after sunrise they are both in the sun all day long until about 30 to 40 minutes before sunset. Prior to moving them, one hive had a small number of SHB present. I swapped the brood boxes on that hive last Saturday and did a thorough inspection also. I found no SHB present. Prior to the move, I'd find 2 or 3 each time I opened the hive. This was my first time to go completely through the hive and I was very pleased with the results I found. The full sun has helped my SHB problem.