|vbaise, You don't want to delete those compressed files.|
"Compress Old Files
Unlike the other categories, Compress Old Files doesn't delete any files from the drive. It compresses files that Windows hasn't accessed for a specified period of time. The files are still available, but there will be a slight increase in access times because the files will be decompressed the next time they are accessed. Note that when Compress Old Files is highlighted an Options button appears. Clicking it will allow you to set the number of days to wait before an unaccessed file is compressed."
If your Computer is hanging up while compressing old files when using Disk Cleanup the link below has a solution.
Disk Cleanup tool stops responding