Thank you for the great tip!
I bought 3 boxes of cereal in 3 separate transactions and yes, I paid 1 cent for each of them.

In my Dominics in Elmhurst (St. Charles & 83rd rd) they adjusted self check line: cash register beeps every time someone uses a coupon (doesn't matter what is the coupon value).

(I know for a fact, not all Dominics self-checkout lines work this way. I was in Chicago yesterday and didn't have this problem (beeping).

So, to avoid nasty conversation with cashier, I use self-check line.
1) I scan the cereal.
2) I scan the coupon -- Cash register beeps and requests assistance.
3) Customer assistant comes and looks at my coupon. She types the coupon amount without any arguing.
4) I scan my preferred card after cashier left.
5) I pay only 1 cent. Although the tax should be 2 cents.
6) I am happy, because I avoided cashier aggravation.

the actual price of the item, I would just buy another item to cover the overage instead of the second thoughts they have about downsizing the amount they have to deduct. Otherwise you have the clerk scrutinizing over it and trying to recall his/her coupon 101 class they just took last week...again. Which by the way at Dominicks, I'm sure they are confusing as heck because of the way they keep interpreting their own rules. The only person that has to know you got a good deal at the time of sale, is you. I know... I'm tempted to scream and shout at the checkout line I was paid to take something home. But there is a time and place for that...in front of your spouse and right here :)