I'm very big on drills with the hands in unison these days. It strengthens the left hand, and is excellent training for playing singles solidly, in time, without rushing. This is a very basic rock drill which I've never seen written or taught, but which I think should be included in the basic ways rock drumming is taught. It probably exists somewhere.
Like I said, it's simple: use my basic rock drill with both hands playing running 8ths in unison, accenting the 2 and 4:
Get my e-book EZ Rock Drumming for a fuller, updated explanation of my basic rock drill, and its variations. Of course you can do this drill with any book of basic rock beats.
Play the hands on the snare and floor tom, or on any two drums. Or any one tom. Or moving between drums. To me there's something rather Joey Baron about this drill— I can't explain it any further than that.
You can improvise additional accents on 2&/4& or &2/&4 to fit around the bass drum part for whichever line of the rock drill you're playing:
Another way of experimenting with the orchestration would be to do something different on the 2 and 4— flamming on the snare drum, or accenting on the snare drum and crash cymbal together:
An excellent endurance drill would be to play pages 14-15 from Syncopation (using my rock beat application above) along with my Bill Frisell/Child At Heart loop.