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!). 

I tried looking also at the drupal statcounter module (http://drupal.org/project/statcounter) but this module does the same thing: puts statcounter in a block.

Anybody here put their counter somewhere where it can stay hidden? I realize this could be an issue with my template, but for those that have sucky templates like mine, is there something one can do?

Also, if I were to use Google Analytics instead of statcounter, can I keep the code invisible, or am I doomed to show it as a block??

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