I just now realized that GNU tar has a --remove-files option. From the man page:
--remove-files Remove files from disk after adding them to the archive.
So when creating a tar archive, the option removes each of the original files as soon as it has been added to the archive. I found it especially useful when dealing with a server that is low on disk space.
$ find . . ./logs ./logs/3.log ./logs/5.log ./logs/2.log ./logs/4.log ./logs/1.log $ tar --remove-files -czf logs.tar.gz logs $ ls logs.tar.gz