Thank you Dan. I was not aware of the "secondary anchor" concept. We also run Desktop Basic version 10.4. The keyboard shortcut is also listed in the local help text - however it does not appear to function. "A" will bring up the box to specify a rotation angle but keying in "S" does nothing at all. How may this be enabled?
Arc PRO however, does bring up the secondary anchor and it looks as if the desired functionality may be obtained with a little practice, even though the rotate handle is only available with the primary anchor being visible.