Hindquarter-in is already mentioned by Salomon de la Broue (1600) and François Robichon de la Guérinière (1733). Both gentlemen had some doubts about this exercise.
Guérinière states that the horse, with its head next to the wall, will move more automatically forward-sideward than move between the riders’ aids. When the wall is then removed, the horse will not respond as well because the horse is used to the support the wall provided.
De la Broue has the same opinion and recommend the hindquarter-in only for horses that are heavy in the hand, but in a way that there is always 1.5 meter between the horse and the wall. Both gentlemen recommended the renvers rather than hindquarter-in.