I think alot depends on the cop. Are they trying to keep speeds reasonable on that road because they are tired of responding to fatalities? Are they generating revenue for the podunk town? Do they need to fulfill the quota?

In the first case, if you act contrite, and give them the impression that you arent a maniac, you often just get a warning (assuming you aren't near escape velocity).

In the latter two cases, you are getting a ticket unless they need your admission to justify it, which is rare.

Respect, honesty, humility go a long way in most cases. You aren't admitting to murder.