Virginiarose, I had seen that video - thanks - but it raised questions for me, which is why I posted.
For example, while she talks about cutting above visible flower buds, the buds on that first scape seem quite a bit lower down than the top leaves below the dead bloom. It would have been helpful to have had a discussion about that - where you can (and can not) expect new flower buds to form. It would also have been helpful to have had closeup shots on the flower stalk illustrating where to cut, or not.
Karen, thanks, I think I understand now - look for the new flower buds. If there aren't any, then cut just a little above the uppermost leaf. (And, I guess, wait and see what develops...)