Earlier in my career I was put on a project from a recently fired developer that was some of most convoluted and buggy code I've ever seen. I and the other developers that were put on the project to save it all lobbied _hard_ to rewrite it from scratch.

We were denied, so we tried to trudge along and ended up rewriting the worst component of the bunch, as it was so buggy that rewriting it and then making facades to maintain the old interface was the only conceivable way to make it work.

It went so well we started doing it to other components, and when two components on each side of the facade had both been rewritten, we found we could get rid of the facade. Without putting the project on stall, over time, we had essentially rewritten the entire thing.

It's a really good way to do things. I've been on rewrites before and they didn't go as well (second syndrome effect, etc).