How to stop WP stripping out empty DIV tags

As anyone who’s ever done any HTML/CSS/jQuery coding will know,
empty DIV tags certainly have their uses.

Using

<div id="placeholder"></div>

for example is a stock standard way of using background images.

Its incredibly frustrating that WordPress WYSIWYG editor
strips these out! You can add them to your page in HTML view
but any time you save in WYSIWYG (or your client does) the tags get
stripped for all eternity.

I’ve found workaround is to put a decimal stop between the tags and
then hide it with

CSS display:none

but it seems a bit kludgy and surely unnecessary?

I DONT wish to go hacking the core code to modify the allowable HTML tags.