Preventing styles goin too far inside the element nest

I have a fairly simply page; it's essentially a gui/dialog
with (lots of...) nested boxed elements on it, which
is working fine.

My problem is that if I try to set a (e.g. font) style
on some text in an outer enclosing div, it propagates
to all enclosed text, no matter how deeply embedded.

I would like to be able to style just the
text that is immediately inside the outer element.

Just to make life harder, it appears that
direct child selectors are not universally
supported...

http://www.quirksmode.org/index.html?/css/contents.html

BugBear