Honestly, there's not much you can do. You're basically at the mercy of the court, which depending on the size of the municipality will make big difference in whether you're given a "good deal" or not. Mid-sized cities and suburban communities in NYS usually have DAs and are more than willing to plea bargain to a lesser (non-point) offense. In these municipalities, there is often too many tickets/violators to conduct bench trials.
The last time my girlfriend went to court in an Albany suburb, there were probably two hundred or more people in attendance for traffic court (with about 2-3 hrs total allotted). Didn't matter the offense or mph over, everyone was offered the chance to plea to a PARKING TICKET! In these situations, you can often negotiate the deal a few weeks before trial or, more often, the day of the trial without a problem.
The worst place to get a ticket in NYS (outside NYC) is a rural town/village, because they have nothing better to do than conduct a couple traffic court cases every few weeks (sad, but true). Often these towns do not have a DA and, instead, the Town/Village Justice will conduct the case. You'll tell your story... the Cop will tell his/her story... and you'll be found guilty. If it is a local cop, you'll sometimes be able to organize a deal through the mail/phone, but if it is a sheriff or State Trooper, they'll probably say "tough luck." Still, try to negotiate a plea bargain beforehand in small town courts, because you'll rarely be given a deal day of in these situations.
Where did you get the ticket, exactly? What agency is the police officer from (village/town, sheriff, or State Trooper)?