I don't know that it so much a function of util as it is number of revolving cards and bank cards with balances. I know that seems like splitting hairs, but I just don't see that much of a difference in util change.
When I had two cards with balances of $350 and $50, that was a util of 0.279%. When the Chase card updated to $0, leaving only the BB card with $350, my util became 0.244%. That's a difference of 0.035%. Granted, for scoring purposes they both rounded up to 1%, but I did gain 2 points for going from two cards with a balance to one.
I think when I went from one revolving account to zero, I got hit with Equifax reason code 17, No recent non-mortgage balance information, or code 24, No recent revolving balances. Or heck, maybe both. 
(See the stickied FICO scoring reason codes for the link listing all the ways you can go wrong with your personal credit, lol.)
I go a little cross-eyed after looking at reason codes for a while, but it's an interesting slant on the different factors that result in our credit scores. IMO, everyone who's curious about FICO scoring should get familiar with these things.
And by the way, the order of the codes isn't relevant. #38 on all three reports is the worst thing you can have. High revolving util is #10. #13 is too-new delinquency. And so forth.
I think I got it for something like $99.95 annually, about equivalent to one beer per month at the bar, just that I don't go there often. 