The tune features "violin, electric guitar, and the echo of distantly otherworld keyboard noise" then it, and the album, "fade into oblivion" with "a lonely piano coda and a desperate plea" to 'Grow old with me'. In his review of "On My Way to Absence" Todd Martens of "Billboard" favorably compares Jurado to Nick Drake, Iron & Wine, Cat Power and Elliott Smith. Brian Howe of Pitchfork writes that "while it isn't Jurado's most daring work, it is among his most immediately engaging" and refers to the album's melody as "rich, fragrant and utterly human". The songs "resonate with the verbal economy and hallucinatory clarity", Howe compares them to the short stories of Raymond Carver. Greg Elias of "The Good 5 Cent Cigar" calls the album "more of a pop album than anything he has done" and "a testament to his ability to maintain artistic integrity in constantly shifting atmospheres" proclaiming that Jurado is "among the best songwriters of his time and ilk". Peter Funk of Stylus calls the album Jurado's "saddest though finest efforts to date". "Uncut" calls "On My Way to Absence" a "self-styled tribute to jealousy" and his "most diverse record yet". However, Reed Fischer from CMJ New Music Monthly writes that Jurado's "detachment is effective about half the time, [but] it breeds indifference" and that the "superb" guest vocals from Rosie Thomas and Eric Bachmann "aren't enough to cobble together the king of compelling, sympathetic portrait he's more than capable of painting".