 Leavin 'is a contemporary R & B and pop music album consisting of twelve tracks, with an additional remix on digital copies. Cole said the material "has given me the opportunity to explore the greatness in the songs of some of our most talented and gifted songwriters," emphasizing the album's "fresh new twist on some great music". The album opens with Cole's cover of Fiona Apple's "Criminal". Len Righi of The Morning Call expressed surprise at Cole's ability to transform the "agonizing, brazen lament" into "a funky, Tina Turner-type, rump-shaker." The second track is a cover of Neil Young's "Old Man"; The Huffington Post's David Munk called it "a personal rumination on her father". The third song, a cover of Aretha Franklin's "Day Dreaming", was recorded after Austin sang it in the studio. Cole said she "added a little bit of a hip-hop feel to it". Richard Harrington of The Washington Post felt that the fourth track, a cover of Shelby Lynne's "Leavin'", "metaphorically put a little distance between the original R & B diva and the pop star Cole". The fifth song is a cover of Ronnie Dyson's "The More You Do It (The More I Like It Done To Me)"; NPR's Jason King attributes the inclusion of "the saucy but largely forgotten Yancy-Jackson mid- '70s track" to Cole's A & R director. The song contains an homage to Cole's previous single "This Will Be (An Everlasting Love)". The seventh track is a cover of Kris Kristofferson and Rita Coolidge's "Loving Arms" (here titled "Lovin 'Arms"), which Verve marketed as inspired by Etta James, allowing Cole "the opportunity to move back to her 70's roots with rich, shimmering vocals".
