I tend to have a lot of lively discussions and part of that was interrupting the other person to react immediately to what s/he said. This was obviously not very polite and also drove the other person into defense, usually resulting in them interrupting me to, making the discussion more aggressive. Not that I disliked that, but it was less productive.
So a couple of years ago I made the conscious decision not to interrupt other people. Not even if they interrupted me. So today if someone interrupts me, I immediately stop talking and listen to what they say.
This can be extremely annoying with someone who interrupts basically every of my sentences without even realizing it, since it makes it hard to ever get to the point I’m trying to make. Also a lot of my arguments get lost simply because the other person moves into another direction.
But in the end it all equals out. My discussion style changed. I used to have discussions where both sides threw arguments at each other, not really reacting to the opponents argument. Today I nail people by asking questions about what they just said. Most people do not have waterproof arguments, so pointing out the weaknesses in their arguments is a more efficient way to indicate that they should reevaluate their position.
It often results in a two-phased discussion. The first part is filled with the other person presenting his/her position and me just reacting to the arguments, hopefully resulting in the impression that I really thought about what was said and raised some concerns. And a second part, where I (now often uninterrupted) propose an alternative idea, ideally already formed so that the concerns from the first part of the discussion have been addressed.
In total the effectiveness of my discussions increased, since the fighting character had to step back. I also get better reactions, since people no longer feel that I try to run them over with a rhetoric steamroller.