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First, remove all suckers! There are usually many of them on the big old trees. They are easy to spot, they point straight up, which would never work. Get rid of them first so that they don't distract you. Done.
Second, take a look at the tree for any branches that have been broken or are damaged.
Third, anything that points down is bad news, weighs down the branch and doesn't get enough sunlight. Snip.
Fourth, prune any branches that cross or rub on each other. Then just use your discretion to choose one or the other, choose the one that is healthier, or balances out the branch better.
Fifth, prune anything that points up. These branches would be prone to breaking when they are loaded with apples, so they need to go.
Sixth, any branches that point back toward the center of the tree.
Seventh, see here is where it gets harder for me. I have to look for narrow crotches and prune them. I do what I can, but I'm not perfect.
Next I look at the height of the tree, if it is too tall and requires a ladder for pruning, thinning and picking, it needs to be cut back. If a tree is too tall, the sprayer isn't going to reach it either.
Finally, for some of our older trees we've had to look at the length of some of the branches. In the first 2 years we lost some limbs, and even an old tree due to weakened limbs that had not been pruned propely for many years. When they get too leggy, they weaken. So I get Matt to cut them back drastically and we try to encourage some interior growth.