This might be a very beginner question but what's the best way to clean a sport route with a very steep overhang? On lesser overhangs when being lowered off the anchors I would always clip a draw to my belay loop and then clip the other end around the rope to guide my down so I could pull my quickdraws off. However on a steep overhang like this one it doesn't seem to work. Gravity takes effect and I still end up getting lowered more or less straight down.

Thanks in Advance

you could climb it again on top rope.

All you have to do is have an attentive belayer stop lowering once you become level with the draw and you pull yourself in. Find a nearby handhold to take tension off of the draw and unclip. Keygate biners make things easier. Do keep yourself clipped into the lowering rope with another draw as you described.

Mike Minson has the best solution. Following is a pain unless you will not fall off. When you fall following it is not always possible to get back on. Better to tram in and clean on the lower.