Nohup or Disown?

In the past when I've started long-running jobs, I've used nohup. But, what if you forget to use nohup or find that a job is taking longer than expected? Today, I learned about disown which allows you to easily prevent a process from being killed when the parent is killed. Ksplice provides a detailed tutorial on using disown. The quick-and-dirty version is:

$ long-running-process.sh
^Z
[1]+  Stopped     sh long-running-process.sh
$ bg
$ disown %1