This is similar to my last question except that my last question included "while running" in the title. I've since learned that this isn't exactly possible.
Here is my understanding of the options (when using LVM for the file system backing).
1.)
Process: Shut down the domain. Create a LVM snapshot. Bring the domain back up. Create a backup from the snapshot. Destroy the snapshot.
Pros: Perfectly consistent backup.
Cons: Obviously, the drawback of this method is that the domain needs to be rebooted every time a backup is performed.
2.)
Process: Run 'xm save' on the domain. Copy the image file and the state file. Run 'xm restore'.
Pros: Less downtime than #1.
Cons: Still "some" downtime plus network connections will be lost. Also, the image will still not necessarily contain a perfectly consistent file system, BUT along with the state file, a consistent image could be created. (We'd be backing up the machine state, memory contents, etc. at the same time.)
3.)
Process: Create an LVM snapshot. Create a backup from the snapshot. Destroy the snapshot.
Pros: No system downtime.
Cons: Backup would be as if the power cord were yanked from the machine, then the drive removed and copied.
4.) Backup from within the domain by whatever process you normally use.
Am I missing or misunderstanding anything?