I've had various things.
"I stopped you because your headlight wasn't working."
"I will reduce your speed on a ticket because you stopped right away, and you won't have to pay expensive fine."
"Come to the court, and we will reduce your ticket to non-moving violation - just pay the fine".
A state trooper pulls out after I ride by him (at legal speed), and follows me a few car lengths behind and in a different lane. Gives up a couple of miles later and stops following.
Oftentimes, when I pull over and stop on a shoulder, a state trooper would stop by to make sure I am OK. I recall one such case. Once, I was doing my thing (if you know what I mean), and stopped on the shoulder to check my radar detector. 10 sec after I stop, a state trooper pulls up behind me. "It's not safe to stop here, and I will just wait till you leave." Well, thank you Sir.
And my favorite: "I will let you go because you didn't run, and stopped right away."