Comment by hobs
This is also what I love about rebuilding some existing architecture that's not working for a business, its doing mostly the second part - the system is working but it - costs too much, is too slow, doesn't realize some goal, etc - and often times a big part of that problem is because the original intent of the author was not expressed properly.
Usually its not enough time and skills to solve the particular problem, but the most satisfying thing is building a new system that expresses the intent of the original author but at 2% of its original resource usage.