StatCounter in block is invisible...but block is not!

So I'm trying to add StatCounter (see for instance: http://www.statcounter.com) code into my drupal project. I see that the StatCounter pages suggest adding it as a block. Unfortunately, my template is such that even if the statcounter code is invisible, it somehow "thinks" there is stuff in the block, so it builds a little block with empty fields (i.e. an empty block, basically just a container) that looks unsightly and I can't get rid of no matter what I do. (Well I can disable the block, but that disables statcounter too!).