I'm facing a situation where there's a part of some code that I'd like to improve: and there are design flaws in the old code that will make it more than just a simple refactoring.

Although the subsystem is a small part of the system, it's used in many different places, and it's complex enough that I know that functionality will be broken. It's the kind of system that would really benefit from TDD but it's not practical to cover all the code that would be affected. There would be no substitute for a thorough round of acceptance testing and whack-a-mole trolling for bugs.

So my manager and I have to make a call about the benefits and risks of this work, which in turn connects to project management issues. I wouldn't want to do this late in the schedule, but would feel more comfortable doing it early. At certain times I might be able to do this work and have very little impact on other developers but at other times it could impair their ability to do work. (Yes, intelligent use of version control could help a lot here, but that takes coordination with the team.)

The point is that it's a team effort. There are some cleanups which are easy and low risk and you should go right ahead and do. Yet, all programmers have a way of underestimating just how much a twisty piece of code that they don't understand does, so you've got to work with your manager and the rest of your team to control risk.