How do I prevent my mouse from waking my Surface Pro 3?

I have a Surface Pro 3 and a Logitech T630 bluetooth mouse. Before that, I used a Microsoft Wedge Mouse, with basically the same problem: As soon as I even touch the mouse, it wakes my Surface. And since the power button for both the Logitech as the Microsoft mouse is on the bottom, it’s impossible to turn it of without waking my Surface.

Normally, you should be able to disable this in the device managament, properties of the device, etc., but with both the logitech and the microsoft mouse, this tick box is not available. Is there any other way? Disabeling bluetooth completely while in sleep would also be an option, but cannot seem to find that either.

edited by moderator: message edited by adamjohnson