Thank you TCH-MikeJ for that important point of clarification! It seems to me, then, that it would be best to do this in the .htaccess for the entire website rather than individually in Wordpress? I can't think of any advantage of doing it from within Wordpress . . . but I'm not really smart on this type of thing.
Also, for other people who come to read this thread, I want to point out that the gzip feature both of the above responders are talking about is not mod_gzip. Mod_gzip is an Apache mod. The above code given by TCH-Don is a php function that uses gzip compression. I followed the link TCH-Don provided and eventually got to here where (if you read far enough down the threat) it is said that mod_gzip is not supported on shared servers.
Unless that has changed it means those of us who use a shared server can't use mod_gzip, but you can use the php function if you are using php. Correct?
Which leads me to the question, could I change the extension of a .html file to .php and have it get gzipped by the php compression? That would be cool.
Thanks