A Query on Oaths

Allow me to pick your collective blog-reading brains if I may.  I mentioned in an earlier post that I'm working on a piece about the federal judicial oath, and a question has arisen in my work.  Federal judges take a judicial oath whose terms are prescribed by 28 USC s. 453.  But in my research, I have noted discussions suggesting that federal judges take both that oath and a "constitutional oath."  In some cases, I've seen suggestions that the language of this oath is fixed by 5 U.S.C. s. 3331.  But that provision applies to officers "in the civil service or uniformed services" only.  And, indeed, much of the language of these discussions is murky, at best, as to whether federal judges really need to take anything other than the judicial oath.

So what gives?  Are Article III judges actually obliged to take anything other than the judicial oath?  If so, what's the authority for this conclusion?  Article VI of the Constitution doesn't seem like a very good answer, since the judicial oath itself binds judges to support the Constitution, so it's not clear why a second oath would be required.  If there is a second, "constitutional" oath, is it fixed by 5 USC s. 3331, or by some other provision, or simply by custom?

Any replies, via the comments or via email, would be appreciated.  I've floated this question on the conlaw listserve but haven't yet gotten satisfactory answers, so this is your chance to surpass the collective wisdom (or apathy) of the constitutional law academy.