Thanks RiBeneke!
From a web search, I came across a British (I'm an American, working in the US of A) design manual, entitled "Design Manual for Concrete Columns" that has an excellent section on computing ultimate moments for concrete-filled pipes. Very interesting, indeed.
For my work, though, I started with allowable stress method, using modular ratio, etc. The British method, as explained in the manual (I think I got it off the Corus Construction web site, but alas, I can't remember nor do I have a record of the link...) is intuitive and jibes well with what I'd expect. It also, bless them, has an extensive table of ultimate moments as well as enough caclulated section property data to verify that my own calcs are correct.
I will, though, bite the bullet and pick up the AISC manual I mentioned, eventually...