It is not uncommon for climbers to have to carry two ropes for rappel. Unless you're on a team of three, having an extra line can be heavy. As such, many people elect to use a tag line with a "reepschnur hitch."
The following video from Outdoor Research and the AMGA show how to do this technique...
In review, the process is:
1) Tie a blocker knot and clip it to the single rated climbing rope with a locker.
2) Tie the tag line to the backside of the blocker knot.
3) Thread both ropes through your belay device. You're rappelling on the "main line," but by threading both, you can decrease the amount the tag line gets hung up.
4) At the bottom, Dale clipped the line through his carabiner to help him remember to take out the blocker knot at the bottom of the system.
It should be noted that super skinny tag lines can easily become a tangled mess. It is strongly recommended that you practice this on smaller climbs, before employing it on a large wall where a tangle might get you stuck out in the dark...
--Jason D. Martin