[7] Inspired by life in her downtown Detroit neighborhood, Davis wrote or cowrote all of the lyrics, aside from "You Haven't Done Nothin'", a cover of the Stevie Wonder song; Big Chief provided the music.

[8][9][10] The Calgary Herald stated: "Going for a bare bones backup of bass, drums and guitar (with occasional keyboards, congas or horns), Davis delivers a raw, riveting blend of funk, R & B, rock, blues and sweet soul music.

"[15] The Toronto Star concluded that "the combination of the band's slightly skewed vision of funk and Davis' straight-up blues delivery makes for an unusual, wide-ranging but completely satisfying album.

"[16] AllMusic wrote that "Davis' singing is just wonderful—she's got a rich, warm voice that she doesn't show off with, avoiding pointless vocal high jumps and wails for confident, often soaring delivery.

"[11] The Chicago Reader called Sunday Morning Music "a harrowing album full of desire and outrage.