Ok... Ricently I've decided to backup my /home/<USER>/ partition on the external HDD.
I have set up default Ubuntu 11.10 backup tool "Deja Dup" to backup:
-every day
-to external HDD
-/home/<USER> (except Trash)
-with encription

It was fine for a week or so... It made first huge backup of whole home and did an incremental every day at night. Then it dicided to make a fresh full backup (for just in case, i guess) and it faild, says "No space left."
A little reseach have shown that there is "No space" in /tmp directory. So I have cleand /tmp and restart the backup -> faild again, I've cleaned the system as much as I can (now it has ~4.7 Gb free for /tmp) and tried again -> faild.

Also, I can't "Revert to previous version" any of the backed up folders for the same reason. Any of the actions with this backup ends up with "No space left."

I have ~400 Gb /home/<USER>
1 Tb external HDD to backup to
~5 Gb free space in tmp

Ok, what do I do?

P.S. If It is the way it suppose to be (/tmp is the same size as backuped folder), then what is the correct way to backup huge "home" folders to external HDD?