Perfors & Navarro (2014) find something interesting in their iterated learning language game: cognitive priors determine the structure of a language, but only in a tight linguistic bottleneck. This means that in when new languages are born with only a few speakers, their shape may be tightly determined by cognitive structures. We see this in in the Al-Sayyid Bedouin Sign Language community [Sandler, Meir, Padden and Aronoff (2005)] and homesign systems [Goldin-Meadow & Mylander (1998)], where canonical word orders are tightly constrained. In ABSL, SOV word order dominated after only a generation of learners in a community with about 150 total signers. In homesign systems, which have at most one native signer and a handful of proficient ones, SOV and SVO word orders dominate.