Mac Encrypted USB drive giving different capacity
You could look to folders that you can zip into a compressed folder. This should give you additional space on disk4, so long as you erase the files that have been added to the compressed zip file. You can either use Compress Files in Finder or zip in Terminal.

UPDATE

While this does not address rsync directly, this is another option that you may consider.

If this is solely a backup, and you are not actively using the data on disk4, i.e. it would only be used to restore lost data, or recover incremental data, then I would say try CrashPlan by Code42. The software is free and you do not need to buy their premium cloud backup services to use the local backup functionality. The only thing is that without the premium plan, I do not think that they unlock the ability to set the backup schedule for local backup. They do however give you a thirty-day free trial for the premium service, so you can determine how important having control over the backup schedule is. 

It works very well, and is very light on resource utilization, so you won't know it is there. I in fact view it as a flaw in the software, as they are only addressing a single core of multicore processors, which can extend initial back up times. You have control over how much you allow CrashPlan to use your systems resources. 

The benefit is that it significantly compresses the data to the backup drive, depending obviously on the data you are backing up. While you cannot use the information directly from Finder, the GUI lets you see the file structure and you can easily restore a single file or the entire disk.