Scott:

Where are these "leaders" located on the tree? Are they all vertically oriented, near the center of the tree, and close to one another? If so, and with all due respect to the Texas A&M system, I would completely remove the two vigorous leaders and leave the least vigorous without any pruning.

Asian pears are like many other fruit trees. If you want to keep them within range so you can prune, thin, pick and spray, vertical growth is not what you want to encourage. You seem to have one leader that has less of a tendency to upward growth, and that is the one most likely to be fruitful and the one I would select. When this leader begins to put on lateral growth, that is where you will pick the most Asian pears.

If you prune back the two vigorous leaders now, in the late dormant season, you will find bushy growth generated at the point of the cut. That will also be true if you cut them off at the base, but you can remedy that by pruning again in late summer, removing all the new growth to discourage them.

For me, the biggest chore with Asian pears every spring is thinning. I have several varieties, and get about 99% pollination, which leads to many fruit clusters with 5-6 small fruits. I have to thin in at least three stages before I get the crop reduced to the point that the fruits can reach their full potential, without breaking branches.

Don Yellman, Great Falls, VA

If you look at the diagram in the Texas A&M website, my trees are in the second winter stage. The leaders are kind of like the ones in the diagram. They are the leaders coming out from the previous year's cut. They are at a wide angle but have the typical pear vertical growth. I probably won't remove the two vigorous leaders now because my trees are only 4 feet high.

In general, do you always cut the leaders' terminals every year to promote lateral development even the leaders did not grow much?

Scott:

I did look at the Texas A&M website on the link you provided, but am still not convinced this is the best way to prune a pear tree. Yes, it will result in more horizontal branches in the center of the tree, but many of them will be growing inward, which is one of the things I try to avoid.

If your trees are only 4 feet tall, you are not really at decision time yet, and you can just about let them do anything. But once they begin to mature, I prune only in late summer. Otherwise, I induce leafy vertical growth that I do not want.

Don Yellman, Great Falls, VA

You want three vertical leaders so that when one of the leaders gets FB then you can cut it out and still have two thirds of the tree left. Having one leader is the last thing you want to do on a pear tree IMHO, just for good measure. And if your tree only grew 12 inches then it is possibly going to runt out on you. Might not be a bad thing if you want a very small tree. I would want a bigger tree so as to get some of it above the frost zone. I think I would cut all three leaders back to one third so as to stimulate growth.
I didn't know you could grow pears at Austin. I thought it was too Weird there. Seriously, I thought you might have too much Cotton Root Rot.
Yes you want to head the leader each dormant to induce lateral branching, but a vigorous growing pear tree is in danger of fire blight.

My Potomac was growing tall and skinny so I cut it back. Now I have 4 good angled branches without a central leader.
So far I can easily reach the entire tree. This will be the 3rd yr I have it so I'm hoping for flowers?