If I can add my two pennyworth - I think owning up to the offence is not always taken as being honest but more as an admission of guilt.
Here's the problem as I see it. You're doing, say, 39mph in a 30 zone and get stopped. Asked, as you always are, what speed you were doing and replying, "39 miles per hour" can easily be met with, "You've admitted an offence of . . . "
BUT - if you answer "30 miles an hour" you are almost certainly insulting the officer's intelligence and he ain't going to like that.
For the years I've been riding and driving whenever I have been stopped for speeding - not very often I hasten to add - in answer to the ubiquitous question, "What speed were you doing?" I have always answered, "It wouldn't be in my interest to admit to anything over the speed limit."
I've always been asked the same question again, sometimes worded in a different way, and always answered the same way but the second time added on the words, "I might have been a bit silly (or stupid, or faster than I should, or whatever that acknowledges you weren't doing it right without actually admitting an offence)"
It's worked for me every time. Either I've been very lucky or there is a bit of logic and reason there. You decide.