Changing page.tpl.php depending on content type - possible?

I'm perplexed - I've always tried to avoid changing the themes I use, but this time I actually need to.
I'm using Flash node to create content type "Flash", which is basically a Flash video. Since these are quite big (I like to make the most of the whole page) I want to make sure that they display without any blocks, and with an absolutely minimal top title (ie where the site name and slogan goes). I had thought of over-riding these by creating my node-flash.tpl.php but it seems that some of this stuff is defined in page.tpl.php and as far as I understand it there can only be one of those: or can I make a special page.tpl.php for Flash content only?