Systematically managing technical debt

We would like to systematically approach removal of technical debt but we are not sure yet how we should actually approach it. One idea was to identify the debt and then create tasks and try to prioritize them. The problem is that there is always something more important than reducing technical debt so this is not the way. Then another idea was to remove the technical debt on particular application when you do some priority work on it. So one would finish the prioritized task on the app and after that do some maintenance work.

How do you approach removing technical debt? Any ideas are welcome.