I’m working now on a page that has a column of boxes styled with sexy shadows and corners and whatnot using the example here. I have to admit, I don’t fully understand how that CSS works, but it looks great.
Inside the topmost box is a text-type input used for searching. That search box is wired up to a YUI autocomplete widget.
Everything works fine in Firefox3 on Mac, FF2 on Windows, Safari on Mac. In IE7 on WinXP, the autocomplete suggestions render underneath the round-cornered boxes, making all but the first one unreadable (although you can still see enough peeking out between boxes that I’m comfortable IE7 really is getting more than one suggestion).
Where could I start looking to correct the problem?
Here’s what success looks like in FF2 on WinXP:

And here’s what failure looks like in IE7:

The working solution I finally implemented was based on reading this explanation over and over again.
In the underlying HTML, all of the blue rounded corner elements are DIVs, and they’re all siblings (all children of the same DIV).
The z-index of the autocomplete div itself (which is the great-great-grandchild of the rounded corner container div) can be arbitrarily high, and it won’t fix this issue, because IE was essentially rendering the entire contents of the search box below the entire contents of the “Vital Stats” box, because both had default z-index, and Vital Stats was later in the HTML.
The trick was to give each of these sibling DIVs (the blue rounded corner containers) descending z-indexes, and mark all of them position:relative. So the blue div that contains the search box is z-index:60, the “Vital Stats” box is z-index:50, “Tags” is z-index:40, and so on.
So, more generally, find the common ancestor of both the element that is getting overlapped and the element that is overlapping. On the immediate children of the common ancestor, apply z-indexes in the order you want content to show up.