what gives??

I sometimes move a few GB back and forth from my home machine to my
lab using the 'net.

My standard practice is to first make a .tar file, to gzip it, and
then to use split, creating 1MB files, which are further reduced to
300 bytes (some, 150 bytes or so, it depends on several indeterminate
factors.)  Then I send those files as one .tar file.

On the other side, the process is reversed.

Now, here is my problem, and thus, my question:

Some of the 1MB files, cut from the gzipped .tar file, are not very
random.  And cause my process trouble (I XOR the input of course, but
that isn't sufficient to depend on.)

To verify this, today I took 260 1MB gzipped files, each part of a
single .tar file, and re-applied gzip.  (It's a simple fast test!)

And guess what, several compressed by as much as 3:1.  What's going
on??

This problem is PRIOR to applying my re-compressor.  So my code isn't
part of the problem.

Anyone know what's going on??