I've tested a few of backup utilities and still haven't found one that would satisfy me.

Almost every one of them has two options:
- full backup - not an option to use frequently
- incremental backup - seems right, but there's one thing about it:
Incremental backup builds on a base of a full backup, backing up only those files, that were created/changed. The thing is, that after some time you've got a lot of unwanted files from the old backups bloating your backup device. Also, if you'd accidentally delete your full (first) backup file, then the differential backups would be corrupted (you wouldn't be able to restore them).

The thing I'm looking for is a program, that would backup files simply by copying them. It would check the backup device whether it contains the file (unchanged):
- if yes, it should proceed to the next file (we've got current version backed up)
- if no, it would copy the file to the backup device
- if the device contains a file that is no longer on our disk, the program would delete it from the backup device

Is there any such utility, that would work this way? If not, do you have any hints on how to backup fairly big amounts of data (around 20gb) quite frequently with incremental backups and not be exposed to those unwanted effects of backup size puffing up?