From the start of “A Quarreling Pair,” which opened on Tuesday at the Brooklyn Academy of Music’s Next Wave Festival, you feel that you have been plunged deep inside a private world. This is partly because its source material, a short puppet play from 1945 by Jane Bowles, depicts a suffocating, insular relationship between two sisters. But it is also because Bill T. Jones, the director and choreographer of this dance-theater adaptation, has lived with the Bowles play for so long — 15 years — that it has transformed itself in his mind, becoming a sort of cryptic shorthand for all manner of riffs.

This is both fascinating and maddening. Or perhaps it is fascinating because it is so maddening, with Mr. Jones careering among high kitsch, odd beauty and oblique social commentary, all within a raucous vaudevillian prism. He isn’t out to soothe any nerves.

Miss Harriet and Miss Rhoda (both brought to wonderfully strange life by the actress Tracy Ann Johnson) are elderly sisters who have lived together, alone, for many years. They are bound by deep affection and deep rancor, and they do not see the world in similar fashion. The play depicts them trapped in an endless cycle of words, always at cross-purposes. But Mr. Jones allows Miss Rhoda to go out into the world, whose “sufferers are always on my mind.”

But first, the stage! A creature of the theater, Mr. Jones naturally sends Miss Rhoda there first. Thank goodness, as this allows Ms. Johnson to sing a delicious rendition of “This Bitter Earth”— or most of it, before her incompetence gets her fired. (Note to aspiring chanteuses: Best not to answer your cellphone during your own song.) She plummets all the way to Mexico, and a vicious run-in with La Torita, an enraged drag queen played by the marvelous Erick Montes.

These and other scenes play out through Janet Wong’s video projections and through dance passages, which are sometimes spare and elegant, like Bjorn G. Amelan’s set, and sometimes coarsely physical and suggestive. Through it all, the connection between the sisters remains the most tangible reality, with Miss Harriet waiting, forlorn but patient, for her sister’s return. Has Miss Rhoda actually gone anywhere, or has she simply slipped through a window of her imagination, a place where the stolid Miss Harriet, with her “gift for contentment,” could never follow?

Mr. Jones’s collaborators, on the other hand, follow with gusto. Most have worked with him for a long time. (Liz Prince’s evocative costumes and Robert Wierzel’s lighting should also get nods.) But the bandleader Christopher William Antonio Lancaster is a relatively new addition, and an exciting one, offering up rich stews of original and appropriated music. Here he is joined by Wynne Bennett and George Lewis Jr., who serves as an M.C. of sorts and whom Mr. Jones should sign to a lengthy contract.

The band’s rendition of Bob Dylan’s “Hard Rain’s A-Gonna Fall,” with Mr. Lewis singing, ushers in a scene of pure poetry, in which the lost, battered Miss Rhoda is swept up in a greater sea of movement. At last, at sea in the world, she finds herself.