I recently upgraded to a 1070, and first time really using Precision (used to use Afterburner)
 
I use a triple monitor set up and frequently have videos/streams open on my other monitors while also playing games. 
If I watch a video fullscreen (ie youtube or twitch) while a game is open, my clock speeds + voltage plummet until the video is either closed or minimized. While this happens, naturally my fps drops sharply in whatever game I'm in.
 
I'm assuming this is due to the software/driver just applying some low power setting when it senses that video playback is happening, but not taking into account that other processes are still active and require more power.
 
Is there anything I can do? I'm currently on the latest driver (368.81), and have reinstalled the software.
 
Edit:
I'm on a freshly installed Windows 10, 64 bit
 

Yep.

Behaviorally, the same thing happens whether the software is open or shutdown entirely.
I currently do not have any other gpu monitoring software to monitor the clock speeds while precision is closed, however the effect is pretty evident.

Thanks. I don't know why I didn't think to try that. Solved the problem.