I was on a rural road by my house last Friday where I thought the speed limit was 55. I spotted two sheriffs coming the opposite direction so I slowed down, but when I passed them one of them made a fast u-turn. When I saw that I just pulled over on to the shoulder and waited. The guy didn't even need to turn on his lights. He took my license and asked me for my proof of insurance. I gave him the license but couldn't find the insurance card. He asked me what I thought the speed limit was, he corrected me and told me it was 50 and that I was going 67. He told me about his concern for my speed and I apologized before he headed back to his car for the 5 second lookup of my record and the obligatory 15 minute break to work on his crossword puzzle.

He came back and told me that he was just giving me a ticket for not having my proof of insurance which isn't really a ticket at all if I am truly insured.
They did the same kind of thing for my wife who was speeding on the same road. We didn't put the new stickers on yet since the weather was still pretty crappy so he gave her a fix-it ticket for that.
My experience is that cops can be pretty cool if you're cool to them. It might also help to have a minor infraction that they can ticket you for instead of the moving violation, as well. I'm not sure about that one, though, so don't blame it on me if it doesn't work.
I was in my Mustang, of course, and my wife was in the Mountaineer.