Not enough free space to restore iphone backup
I've encountered the following problem with my iphone 5s. When I try to restore a backup using iTunes, the process starts in iTunes, the iphone restarts, but then I get an error message: iTunes could not restore the iphone because not enough free space is available on the iPhone. Please see screenshot below.
I've tried to the same thing on my wife's iphone 6 and her mac. Exactly the same result. I could not restore a backup made minutes before trying to restore it.
To clarify, I am using the latest software (iTunes, IOS, MacOS), the backup is not larger than the storage space on my iPhone and it is a backup from the same iPhone to which I am trying to restore it.
Surely Apple doesn't expect me to restore my iphone first (i.e. reset to factory settings and erase all data) before restoring a backup? I'm reluctant to reset it to factory settings as I will have lost a lot of data if the backup still doesn't restore...
I've read all the relevant threads on Apple support communities (at least I think I have) and no one has provided a solution to this problem.
Can anyone help please?
Thanks,
Jan
iPhone 5s, iOS 7.0.4