Quick copy of time machine backups

What is the fastest way to copy a time machine backup drive to another disk for safekeeping? I bought a hard drive to copy my current time machine backups but it was going to take forever and I didn't want to be without my time machine that long. I tried to just copy by copying the subfolder (e.g. Macintosh HD) but it filled the new disk after only copying about 1/20 of the folders. That makes no sense if they are the same size drives! Does time machine somehow shrink them? I just want a backup before I get the dreaded "Time Machine must create a new backup" and I lose the backups I have.