A Strip the Willow where the lady first strips down the men, the man strips up the ladies and then both strip down the set together ...
Described in the Community Dances Manual, book III as being the English version of "Strip the Willow". In this instance, the "Strip the Willow" is referring to the Scottish dance rather than "Strip the Willow" as a figure.
Here the bold shows the words 'as published', the notes and annotations hopefully make things easier.
The 'next' couple, the one waiting for their go can get going with the single reel when the first couple are out the way. A good guess is when they are half way down the set, you don't want to start too early and risk catching them up (it gets messy). You might also want to wait until the start of the phrase of music.
The strip the willow figure goes back a long way, there's a reasonably clear description in Trenchmore, published in the 2nd Edition of Playford (1652). The third part of which is:
Which is, perhaps, a description of the man stripping the willow down the set followed by the woman stripping the willow up. Trenchmore can be also be traced back quite a bit further
Halfway through the dance, the caller may cry Double Reels only, or something similar. You then skip the dancing down an up with Single Reels. When you are at the top of the set, you wait (a little) until the way is clear and the start a Double Reel, the next couple waits (a little) and starts a Double Reel, then the next...
It goes faster and more furious and you find yourself doing a short set version of the Orcadian Strip the Willow
The 'Strip the Willow' figure is quite popular. The 'single reel' is characteristic of the Drops of Brandy dance but you'll find the 'double reel' appearing elsewhere; the Stoke Golding Country Dance, the Foula Reel, in some variations of Sir Roger de Coverley and, of course, writ large in the Orcadian Strip the Willow