Mavericks -> AppleTV Airplay & Parallels & Menu Bars

I just upgraded my iMac (2012) to Mavericks.
I'm playing with the Airplay mirroring to the Apple TV.
I can extend my desktop to it, giving me 3 screens (iMac, external, and tv) and that's neat.

HOWEVER, when I put a Parallels Destop 8 window on the TV and go full screen, I still have the apple menu bar there. When Airplay is turned off, there's no menu bar. I'd prefer for there not to be one.

Any ideas on how to fix this? googling hasn't turned up anything.

EDIT: Further testing seems to point to this being parallels specific...Quicktime Player, Preview, and Firefox get rid of the menu bar in full screen mode.

AND, realizing it was a Parallels and not Mavericks or Airplay made it an easy google search to find :

http://forum.parallels.com/showthread.php?208334-Disable-Apple-Menu-amp-Dock-In-Lion-Full-Screen

With the Additional bit: Checkmark "Use all displays in full screen."