Extra "/" in URLs

Howdy :)

My SWFs are not showing up with SWFTools (which is pretty bizarre because it worked in an earlier incarnation of the site)
I found there is an extra "/" in the URL right before the file name:

<script type="text/javascript">
swfobject.embedSWF("http://context.tst/files/slideshow//cummings.swf", "swfobject2-id-12213596061", "500", "405", "7", "", { "width": "500", "height": "405" }, { "wmode": "opaque", "bgcolor": "#2c4d56", "menu": "false", "play": "true", "loop": "false", "quality": "autohigh", "align": "l", "salign": "tl", "scale": "showall", "swliveconnect": "default", "version": "7", "allowfullscreen": "true", "width": "500", "height": "405", "base": "http://context.tst/files/slideshow/", "src": "http://context.tst/files/slideshow//cummings.swf" }, { "id": "swf12213596061" });
</script>

And yes, I checked - I did not have any trailing slashes in my settings.php file:

$conf = array(
    'swftools_media_url' => 'http://context.tst/files/slideshow', // No trailing slashes!
 );

I think I may have encountered this issue elsewhere, but just couldn't find it. I'd be grateful if someone just pointed me in the right direction.

Cheers and thanks!