mouse-face vs. transient-mark-mode

[JD Smith]

When an overlay property of 'mouse-face 'highlight is set on a line,
and transient mark mode is on, and you attempt to drag out a new
region in the line, the region mark overlay does not show, and
significant flickering occurs as you drag the mouse inside the
highlighted text.  As soon as the mouse moves out of the mouse-face
area (either during the drag or after it's completed), the mark face
is visible.  The flickering is present even when transient-mark-mode
is disabled..

Is it possible to set a priority on either mouse-face or the region
highlight property to have the former yield to the latter?

Thanks,

JD