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I have had a similar problem using a dropdown menu postioned above a frameless scrolling box (created combinig css fixed positioning and a css/javascript hack for IE).
I ended up setting z-index:5 for the dropdown menu and other fixed elements while setting z-index:3 for the scrolling box.
It tested allright in IE, Netscape, Opera and Mozilla.
Hope it works with i-Frames too.
Good luck.
However, I have usually had some good reason to use an iframe (not layout - rather, saving bandwith with a huge js menu that's the same all the time, that kind of thing). If I don't, I just use a div with style="overflow: scroll;". I just looked at one of such things I've got in Opera since you noted it there could be issues, and it looks just fine - you find a lot of advice on the web about dealing with older versions of opera, but it seems most operaites keep fairly up-to-date versions, and don't go for eons without updating. 'Old Opera' users would probably amount to less than a quarter of a percent, I'd guess. My version of opera is 7.54 u2 Linux.
Doing things with an iframe require a separate request to the webserver, and make your whole thing more complicated, unless you have very good reasons to use them.