Yes indeed, TERPS generally has tighter tolerances than ICAO, so 600'-2sm is the minimum for the catagory D circling maneuver. And for our friends from afar, if they come to the USA to do an FAA type rating on a heavy jet, and stray beyond 2 miles during the required circling approach, they ah......fail. The approach is generally done all engines, but most FAA guys I know want to see it done with one engine inop on three or four engine aircraft.
On the newer simulators, this is a very good confidence-building exercise and, if properly done, results in smiles all 'round.