Take a Rest
One thing that gets very little (no) discussion here is the value of taking a good rest when shooting at deer. One of the things I do while moving is try to pick the next good rest that will be at hand if a deer pops up when I get to that next spot. Even in dense areas, this is not a bad idea. It forces you to think ahead and to look. In open areas, it's even more valuable because you may really need that additional steady platform for a long shot. Over the years, I have used rocks, tree limbs, tree trunks, barbed wire fences (the posts and even the wire), sage brush, just about anything that might add even just a little stability to my hold. If I know I will most likely get a long shot (like while hunting pronghorns), I attach a bipod to my rifle. At other times, I carry home-made three-legged shooting sticks. This is almost as good as shooting from sand bags on a bench. It also gives a lot of confidence before and after the shot.