Speeding tickets - and what can happen once they are issued, varies by jurisdiction. Typically, once a ticket is issued, an officer can't rescind it without a major headache. I'd pretty much consider that option gone. I say that based on family members and friends who are/were cops/troopers.
In CT, if you contest a ticket you get a court date. If you know someone in the state attorney's office, you can get them to drop the charge and the ticket is gone with nothing on your record. If you aren't lucky enough to be able to go down that route, you show up to court at your assigned date/time and you speak to the prosecutor first. If you have a clean/relatively clean record, you can likely make a deal - i.e. donate $X to a charity, come back and show me the receipt and we'll drop the charges. IME, there was like a united way desk on site and everything was done in a few minutes. (Don't forget to save your receipt if you itemize). One other time they ran it a bit differently, and a magistrate had to approve the deal - they didn't allow the prosecutor to cut me as much slack and I had to pay a bit more.
In NY, there are lots of small municipal courts. You show up and before your case is called before a magistrate you speak with the officer who issued the ticket. The one time I had to do that he was impressed that I actually showed (and drove a bit of a distance to do so) and we agreed to a reduced charge (inexpensive parking violation).
I've never done a name drop, but I used to have police stuff in my car - e.g., nearby city uniform arm band or hat. If pulled over it would inevitably lead to "So who's the cop?" and saved my ass a number of times.
Now that I've moved out of state (and am a bit older and wiser) I'm past that stage. The Valentine 1 helps too.