OS X Mavericks :: Disk Utility Refuses To Copy 164 GB To 318 GB Volume

I use Disk Utility (stand alone, on a USB key) to make backups of my system disk to an external disk and then transfer it from my home system to a MacBook and vice-versa when I need to travel. 

Recently, I upgraded from 10.9.2 to 10.9.3 and, not long later, to 10.9.4. In the same period, I also had an increase (not a very big one, just a few GB, less than 15) in the occupied space of that system disk. The current amount of data on it is 164.64 GB. 

I'm not sure if my problem comes from the sub-version upgrade, from the increase in data size, from both, or from something else. The home computer is an iMac with a 318.88 GB internal disk. The MacBook has a 500 GB internal disk. The partitions used on the external disk to make bootable backups are 400 GB big. 

I can backup both internal disks to the external partitions (and boot on the resulting external disk when I check that it is usable). I can also copy the external backups to the MacBook system disk and boot on the result without problem. 

But, recently, Disk Utility has started to refuse copying the content of the external backup partitions to the internal disk of the home system. It says there is insufficient space on the target volume. If the error message is correct, it means that I cannot backup 164.64 GB of data on a 318.88 GB volume! 

For the record, the external backup partitions are OK when verified with SOS. 

Info:
iMac, OS X Mavericks (10.9.4), 4 GB memory