rappelling on an overhanging wall

Yesterday I found myself in a new, slightly sketchy situation. Scenario: Rapped off the top of a multipitch climb where rap line moves from the top rappel station, over a bulge then down overhanging terrain so that the rappel is free hanging. To reach the mid station, I had to swing into the wall to reach the anchors. As I went off rappel I let go of one strand of the rope and it promptly swung out into space about 20 feet from my perch. Shit. I was the first one down so my partner was able to rappel down and swing into the anchor and we made it down safely after some good communication and white knuckles, but it got me thinking. If I had been the second one down and this happened, we could be in some shit. For the sake of my question let's assume that I lost control of both strands (in reality, I only lost one strand but it had a big ol' knot in the end so pulling the rope and resetting the rap was not an option).

Is there a common procedure to prevent this from happening? I was thinking maybe the first one down could have both ends tied to their harness? but maybe that would create more problems with snags and rope management. I am not sure. Or is this just one of those situations that you can't f up?

Prior to untying knots from my harness or coming off rappel I usually take some of the excess rope and tie a quick knot and clip it to my harness just to maintain security of the rope. I believe that an easy solution to your question is that, before coming off rappel you can just take the excess rope below your rappel device and tie it off.

Hahah so simple and easy. I guess I do that already when setting up the first rappel, I need to do it at each station. Thanks.

Andy, the following is commonly done on an overhanging wall or a traverse where letting go of the ropes might put the team in a bad situation.

First person raps down to next station. Removes belay plate. THEN removes backup prusik. (The belay plate comes off first because removing it is takes two hands and is therefore the kind of operation that will make her drop the rope). She then removes the knot in the end of the rope, threads the rope to be pulled through the chains and ties the ends of the ropes together under the chains. This is normal practice - you thread the next station before the second person raps.

The next person down can then be pulled in on the ropes and the ropes can't be lost to the wind.

Once the second person down, untie knot and pull rope. Note that because the ends were tied together rather than a knot in each end, you won't forget to remove the knot before pulling.

In some places where the wall is so steep runners need to be placed on the way down to keep the climber near the wall, lowering both people can make more sense than rapping.