When I got my 4061's, I ran them into my pre and listened with headphones as I handled them. They are *quiet*. I did the same thing with my borrowed AT853, aka SP-CMC4's, and they were very very sensitive. Touching the cables near the body, the body, etc. It is a big advantage of the 4061 that is not often mentioned.
I'm not sure how to improve the AT's.. Make sure your cable is secured shortly after exiting the body?