Rsync useful w/ encrypted files

Is rsync efficient for transferring encrypted files? More specifically:

• I encrypt 'x' with my public key and call the result 'y'.
• I rsync 'y' to my backup server.
• 'x' changes slightly
• I encrypt the modified 'x' and rsync the modified 'y' to my backup server.

Is this efficient? I know a small change in 'x' yields a large change
in 'y', but is the change localized? Or has 'y' changed so thoroughly
that rsync is not much better than scp?

I currently backup my "critical" files by tarring/bzipping them
nightly, then encrypting the .tar.bz file and rsync'ing it to my
backup server.

Many of the individual files don't change, but, of course, the tar
file changes if even one of the files change.

Is this efficient? Should I be encrypting and backing up each file
individually? That way, unchanged files will take no time to rsync.

Edit to add more information:

• The source is my home machine. I own it and consider it secure.

• The target is a colocated server. It's mine, but the colocation
  company could see any/all network traffic and anything on that
  machine's hard drive.

• The source has very little free space. I don't want to halve its
  space by storing an encrypted backup on it.

• The target has a lot of space.

Any thoughts based on this new info?