It's not true that there is no oxygen in the lungs on exhale. Yes, there is less, but the lungs never empty of air or oxygen, at least with normal breathing. Therefore I don't believe it's an absolute given that the deer will drop any quicker if shot on exhale than any other part of the breathing cycle. Although I remain skeptical, for the sake of arguement, I'll grant that it may TEND to drop a LITTLE faster, and TEND to have a greater percentage of dropping on the spot. But I don't believe it will be an absolute night and day difference with a shot taken at any other point of the breathing cycle. Any difference in the deer's response to the fatal wound will be marginal at best.

But I've never done it, so all of my opinion is theoretical, based on my knowledge of respiratory anatomy and physoilogy. - So the real question is: what is the field experience on this? Has it been done by reliable experts so many times that they can say that it works a LOT better than just shooting it? Does it work ALL THE TIME? I remain skeptical but will be interested to be proven wrong.

I stick to my point: Assuming you have a GOOD SIGHT on the animal and a good shot set up (notice I'm not talking about not being patient - patience and making a good shot is absolutely a given), I believe your best bet is to shoot when you're ready. I believe the benefit of "shooting on the exhale" if there is indeed any benefit, is counteracted by too many chances that the deer will startle (from yourself or something else), will move and/or run off. Also, the longer you try to hold a good aim, the more chance something will cause you to become unsteady. Just one example is your own breathing, or lack of breathing. Other examples are a breeze coming on and moving your stand or a branch moving into the path of your bullet or arrow - you can think of many others, I'm sure.

I think it's best to carefully set up a good shot and take it at the point you're confident you're on the kill zone. Waiting for exhale has more POTENTIAL risk than POTENTIAL benefit, imho.