Hi Peter and everyone!
I have a dog that pulls. He is not even a dominant one among my 3 dogs.
In fact, pulling when walking has nothing to do with Alpha, dominant, challenging the Alpha position, etc. It is just because the dog is so excited and anxious to see what's out there. To prove this, doesn't your dog pull more on the way to the park than on the way back home? Doesn't he pull stronger when he sees a squirrel or a cat?
Dogs need to learn to walk slower to keep up with us humans who have only 2 legs. When they pull, just stop with a jerk, or start walking to the opposite direction. If you let your dog drag you, he will learn that dragging you is the way he can get where he wants to go. Don't let him learn the bad habit. Teach him that if he pulls he will not only get anywhere but also it will slow him down by going backwards! Do this from the very beginning of your walk when you still have alot of strength
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Repeat this stopping/going backwards every time he pulls. You and your dog won't go very far at the beginning. Pretty soon, your dog starts realizing (I hope) that you let him go forward when he is not pulling hard. Depending on how much hard wired your dog is, how obedient he is, how curious/obsessed with squirrels he is, it can take weeks for him to realize this but don't give up.
In the mean time, you can practice "loose leash walk" or "heel walk" inside the house using treats. This is helpful because your dog learns to pay attention to you when you give him a command. When you want your dog to walk slowly give him a command "Easy". Once he learns how to walk loose leash, it will be a good reminder on your walk. As soon as he starts pulling you, you can tell him to be "Easy". My other two dogs can walk off-leash on the bike path and when they start going too fast I can just control them by saying "Easy" and they will slow down.
I don't know why but my male dog still hasn't learned loose leash walk. He pulls but he is getting better with the above-mentioned stopping/going backward method.
I found harness is not helpful at all as far as stop pulling is concerned. It almost seems to help the dog to pull more. When you think of sledding dogs you will see why. They are wearing harness and it is meant for pulling. I would just use a regular collar.
Good luck
