Many states have a "Traffic School" that you can take if 1) you plead guilty 2) it's your "first offense".
This amounts to a probation, usually for a year, after which time the ticket is dropped. In Illinois, this is not reported to the Secretary of State (or your insurance).
Keep in mind that if you fight the ticket and lose, you'll also have to pay court costs ... which can more than double the ticket (depends on city, county, state ... charges vary).
Traffic School / pleading guilty will also be the fine + costs, but the costs for a summary trial (if you plead guilty at the arraignment, the process stops there) are much less than the costs for requesting a trail by {jury, affadavit, anything that costs the court more money to stage}.
And, it's not that us "Traffic Nazis" don't speed, it's that when we get caught, we admit it and take the consequences. It's a "grown-up thing."
The court is never going to let you slide just because you felt you were still being safe. One person's version of "safe" can easily be "reckless" in the eyes of the arresting officer and the state.
Good Luck
Scott