It was on Prestige 7361 and Stateside 10150, and he did both.
According to Bruyninckx the big band parts were recorded July 14, 1964 in Stockholm, the parts of Grachan Moncur and and Cecil Payne were overdubbed in New York during autumn of 1964, as were the Swedish soloist in Stockholm.
Never heard that one but wonder how organic it sounds with this triple recording procedure.
Oh well I found out too late , ended up getting the Stateside Lp of this (cheap) on ebay before I read all these negative comments about the session. Penguin give it a decent three stars, I'll judge for my self soon enough.