Problems with large compressed binaries when converting from svn

I'm converting from svn and I've run into a problem with tar.gz and tar.bz2 compressed files.

(This is a separate but only slightly related to previous post).

In subversion we committed large tar.bz2/gz files. These files would change relatively rarely, but only very slightly. The trouble with the tar.bz2 format is that if the first byte changes, then the rest of the file will also be different. .zip does not have this problem, but .zip isn't a very friendly format for our purposes.

Later on the tar.bz2/gz files started to change fairly often, but harddrives get bigger much more quickly than the .svn repository grows so we just kept doing things the same way rather than reeducate and reengineer the procedures.

With .git we need to handle this differently somehow.

Does git have some capability to store diffs of compressed files efficiently?

The only other alternative I can think of is to commit uncompressed .tar files which is a bit of a bump in the road, but I suppose could be made to work.