"Let them settle it." This is the long standing way; let the dogs settle it on their own. Many people still believe that this is the way to settle disputes among dogs. But it is never a good idea; duking it out can have a snowball effect; once they start it just keeps growing. I do not allow nonsense in my house. That means that growls are fine but that is where I draw the line. Of course I have no refereeing to do with Luke and Elsa as they are a match made in heaven but when I had Tilley, Jessie and Luke; there were a few times when I had to step in. Jessie was a very dominant little dog and every once in a while she would like to throw her 15 lbs of weight around. I allowed a little of her displays; most was directed at Luke when he was young. He loved to push her buttons.
As far as Tilley and Jessie were concerned; they had an understanding. Tilley was very happy just being, she had no desire for position within the pack. Jessie was the boss, she wanted and needed to be the boss. But if Jessie tried to discipline Tilley harshly; I could see that it was crossing an invisible line for Tilley. She was fine with a little growl or communication but anything more in Tilley's eyes was uncalled for. I never allowed anything more than an initial communication. Dogs need to communicate and if you take that away, things can go very wrong. I know many people who say "no growling allowed in my house." This can leave the dogs frustrated and confused which then leads to aggression. It also puts you in a handicapped position as far as knowing what's going on.
I am often asked about letting them settle it. No, do not let them settle it. Once dogs fight to settle a conflict; it can become a more regular occurrence. I have seen dogs who lived together for years without any issues until one fight. Then the fighting came more often until one ended up in the emergency room. At this point the dogs lived separately; and the owner did the juggling routine that I am not a fan of. Each dog on opposite sides of the house. The problem with this is that it is not a great way for a dog to live and there is going to be a slip up inevitably.
Probably the biggest problem I see as far as stepping in is with the humans disciplining the wrong dog. I cannot tell you how many times I see people disciplining an adult dog in the family when they bring home a new puppy. The new puppy is testing the waters and pushing the adult; when the adult growls as it should, the humans discipline it for doing so. So the puppy pushes more and the adult feels the need to speak louder which only results in more trouble from the humans. The cycle continues until you end up with an obnoxious puppy and time bomb adult.
When you bring home a new puppy, let your existing adult teach. It is their job and right to show the new comer the ropes. If the puppy is not listening to the older dog then you need to step in. Some adults dogs won't appropriately discipline and need our assistance. If you have a boisterous puppy that doesn't listen to your older dog then you need to step in. When we brought Elsa into the house I had to be very careful with her and Tilley. Tilley growled but that was not enough to reflect much of Elsa's enthusiasm. With Tilley suffering from Vestibular disease I had to constantly be on my toes. Elsa learned very quickly who she could rough house with and who was to be left alone.
Letting them duke it out to come to a hierarchy understanding is not the way to go. We are the leaders of the pack and as such, we make the rules. Enforce them.