Madrid Night Bus to Airport???

Does anyone know if there is a night bus to the airport? I have a flight at 6am this sunday and I really don´t want to pay for a taxi or stay for hours waiting in the airport.

I am having a little trouble finding out if there is a night bus that goes to the airport and where it leaves from (and if there is one close to my neighborhood...Carabanchel)

Any help would be really nice!

thanks!

http://www.madridman.com/ubb/ultimatebb.php?ubb=get_topic;f=3;t=001644;p=2