Anyway, here's a very simple lick that I steal all the time. It's from the tune, "What Would You Say," on the album, "Under the Table and Dreaming."
This lick occurs at about the 3:07 mark.
Okay, after you listen to it, here is one major thing to notice: the bass drum note just before count 4 should be played as a part of the snare drum pattern. If you connect the three notes on the snare (starting on 3), the kick note, then the snare/splash on 4, it's a five note pattern and should be played as such.
Practice getting it smooth and easy. This fill leaves a nice bit of space between count 4 and the next count 1, a tactic that Carter occasionally uses to signify the beginning of a new phrase.
And as I always say, space is just as important as sound if you want to be a good communicator.