How to negotiate - what's your approach?

How to negotiate, especially in a tough situation? What is *tough* for you, anyway? 

I always think back to this episode we had with one of our landlords. 

We were renting an apartment, and while there was not much of a backyard, there was a big tree next to the house, that would cast wonderful shadow over the porch, and helped us survive summer heat. Even with the air conditioner set up on high, one doesn't want to be trapped inside on a summer day, so we practically moved to the porch. If it wasn't for the tree, we would spend our summer inside our bedrooms.

The owner of the adjuscent property had just built a new construction, and was not happy with "our" tree, (which grew on the border of two properties and was actually encroaching his, couple of branches were casting shadow over his new landscaping project).  He called our landlord for a talk. He wanted the tree removed.

They scheduled to meet in the morning of the next day, and we all made sure we were home, and looking out the windows, since the fate of the tree was at stake.

The two landlords met, outside, by the tree. The *other* landlord arrived all charged up. He started pointing at the tree, yelling that "IT'S OLD! IT'S GOING TO FALL! CAUSE DAMAGE! TO EVERYONE! TAKE IT DOWN! NOW"

*Our* landlord kept looking at the tree, and said "It's a beautiful tree... I like it..."     

Then conversation went along these lines:

 - TAKE IT DOWN! IT'S 200 YEARS OLD! IT'S ROTTEN!

 - ...I like this tree, very beautiful... 

 - DON'T YOU HEAR ME? NEXT STRONG WIND - AND IT WILL FALL! HERE, RIGHT THERE! (he also tried to describe where exactly it is supposed to fall)

 - ...A very nice tree... 

I don't have to continue, it went for a while in the same manner. The *other* landlord described different bad case scenarios, all while shouting, and trying to intimidate *our* landlord by all kinds of legal repercussions that might follow. He had a point - the tree WAS encroaching, it WAS rather old, and MIGHT have caused damage to his new construction, if it fell. 

*Our* landlord agreed to call an arborist for a professional opinion, who evaluated the tree and said there is no danger and no immediate need to take the tree down. They cut the encroaching branches, and that was the end of the story. 

Of course we as tenants were extremely happy that the tree stayed. It was a beautiful tree, very old! We liked it!

I also liked how our landlord handled this. He did what was necessary, because the other person had a valid concern, but he also kept the tree. And I think he *won*, over the *tough guy*. I put this strategy to a good use afterwards...

"I like this tree... Very beautiful..."