Though the song had been introduced (in embryonic form) on the tour to support 1975'sThe Hissing of Summer Lawns, "Coyote" was a significant musical departure: where Hissing was ornate with pianos, layered vocals and percussion, "Coyote" was stripped down to electric and acoustic guitars and a fretless bass guitar played by legendary virtuoso Jaco Pastorius. In a sense, this was similar to Mitchell's early albums, but the sound was extremely spacious, even repetitive, with the verses made much longer and more like a long story. Thus, although this is one of the faster-tempo songs on Hejira, it still lasts for an even five minutes. Mitchell's guitar itself was in an unusual (low to high) C-G-D-F-C-E tuning (the same as in the song Ladies of the Canyon) - presumably a type of open tuning designed to play a seventh, ninth, or even eleventh chord.
Lyrically, "Coyote" is concerned with the difficulty of establishing any sort of connection with people who come from "different sets of circumstance" (as the song has it). In particular it describes an encounter (which turns into a one-night stand) between the narrator (possibly meant to be Mitchell herself as there is a reference in the lyrics to her coming home from the studio) and "Coyote", a ranch worker. In Chris O'Dell's 2009 autobiography Miss O'Dell she details an affair she had with married playwright Sam Shepard and states that Shepard then cheated on her with Joni Mitchell. O'Dell claims that "Coyote" is written about Sam Shepard. Coyote represents nature contrasted with the narrator's big city (presumably LA) life where "pills and powders" are necessary to "get them through this passion play". The aforementioned line is also a reference to Bob Dylan's Rolling Thunder Revue, which Mitchell was a part of in the fall of 1975.