In this particular situation, I do not have a choice about the DOCTYPE. I cannot use one. It's a weird situation, but it is what it is.
We have some CSS which uses child selectors ("p > a > span", etc.). These worked in IE7, even though we didn't have a DOCTYPE...and then they suddenly stopped working. Something we did caused IE7 to go into quirks mode, and I don't know what that thing was.
I did this:
alert(document.compatMode);
And it came back with "BackCompat," so I know we're in quirks mode, which would make sense because we don't have a DOCTYPE. But we haven't had a DOCTYPE all along, and this was working, which tells me there's some other way to get IE7 out of quirks mode.