kimberly, unfortunately it's not currently possible to reference something like 'last Sunday' (which I think is what would be needed to make this work) -- it only knows when the upcoming Sunday will be.

If anyone can think of anything creative that might work, please feel free to post (I've seen a number of creative queries posted here that I would never have thought of myself :)

This is maybe a long shot, and I don't really have a good way of testing, but how about something like:
status:completed
AND completedWithin:"2 weeks of Sunday"
AND NOT completedWithin:"1 week of Sunday"

if this works, technically it would grab items completed in the weeks before and after the current week, but unless you are completing items in the future, it just may be a solution.

erik, this is an awesome idea -- very creative!

I tried this out in my account with:

status:completed AND completedWithin:"2 weeks of Sunday" NOT completedWithin:"1 week of Sunday"

(exactly the same, just taking out the 'AND' directly before the 'NOT')

It's showing all tasks completed from Mon 25th Sep to Sun 1st Oct inclusive, which looks right to me -- thanks for sharing this great solution.

Like so many clever ideas, Erik, that sure looks simple when you see it, but wow, I wouldn't have thought of that. Thank you for sharing this idea.