It doesn't have to be a run, just by the by, as you mentioned with the jumprope thing. Every morning I do 15-20 minutes of agility/speed drills on an agility ladder, and that works well for me (partially because it's less impact, and I have a bad knee, like a lot of lifters).
I also recently tried a routine called the Tabata program or something like that -
There's a couple articles about it (ignore all the junk on the second one). If anyone who reads that sees a glaring problem with that training style, then I guess that's my bad - but having tried it I'm inclined to say it works pretty well. Just a few thoughts on alternatives to straight-up running.