A narrower connection specifically between North American Na-Dené and Siberian Yeniseian (the Dené–Yeniseian languages hypothesis) was proposed by Edward Vajda in 2008, and has met with some acceptance within the community of professional linguists.

According to Swadesh (1959: 114), it included "Basque, the Caucasian languages, Ural-Altaic, Dravidian, Tibeto-Burman, Chinese, Austronesian, Japanese, Chukchi (Siberia), Eskimo-Aleut, Wakash, and Na-Dene", and possibly "Sumerian".

Swadesh's colleague Mary Haas[citation needed] attributes the origin of the Basque-Dennean hypothesis to Edward Sapir.

[8] In 1996, John D. Bengtson added the Vasconic languages (including Basque, its extinct relative or ancestor Aquitanian, and possibly Iberian), and in 1997 he proposed the inclusion of Burushaski.

[16] According to him, it is as yet premature to propose other nodes or subgroupings, but he notes that Sumerian seems to share the same number of isoglosses with the (geographically) western branches as with the eastern ones:[17] John Bengtson (2008)[18] proposes that, within Dené–Caucasian, the Caucasian languages form a branch together with Basque and Burushaski, based on many shared word roots as well as shared grammar such as: George van Driem has proposed that the Yeniseian languages are the closest known relatives of Burushaski, based on a small number of similarities in grammar and lexicon.