John T. Davis from
Austin American Statesman complimented "Constant Craving" as "a song graced by a compelling melody and a vocal brimming with yearning."
Larry Flick from
Billboard magazine stated, "There is no denying the
rootsy, down-home quality of this wonderfully produced tune. Lang's distinctive voice is woven into spiraling multitracked harmonies, wafting over a base of acoustic guitar strumming and subtle and
xylophone interludes." Steve Morse from
Boston Globe named it the best song of the
album, declaring it as "a romantic number that's also the only rhythmic tune of the bunch." Clark and DeVaney from
Cash Box named it Pick of the Week and a "standout" of the album. A reviewer from
Daily Mirror described it as "haunting". Rufer and Fell from the
Gavin Report commented, "k.d.'s forsaken
country for a straight pop format that will finally win her the mass audience she's deserved. This track showcases her wonderful voice in solo and multi-part harmonies." Pan-European magazine
Music & Media described it as "a
Brecht/
Weil on the prairie type of song—is likely to be lang's first hit in the UK and in Ireland". On the album review, a
Music & Media editor wrote, "Tales from the new west. La lang has changed her position on horseback for a more comfortable seat on the coach. In mind, she's singing in some
Paris café in the decadent '20s." John Milward from
Rolling Stone felt the song is "more elusive", "but there's no denying the lift of its propulsive rhythms and joyful harmonies." David Bauder from
The Salt Lake Tribune praised "Constant Craving" as one of lang's best songs, remarking that it "concludes that a sense of longing is an inevitable part of life." ==Retrospective response==