deeper - 9:33 am on Jun 30, 2013 (gmt 0)
With my suggestion I only refer to the recommendation of removing before disavowing in order to show your own work. Of course it is not bad to do it parallel and Google will realize the removals later, but if you intend to show your own work clearly and immediately it may be an idea to wait.
I guess Google not only realizes that the disavowed links are already gone, they also know that they were alive only some weeks before. This way you generate a clear signal of having done your job exactly as Google recommended it.
Btw, there is a good video of MC introducing the most important disavowing mistakes. I think MC released just two weeks ago.