On her 2008 debut, 19, Adele included one cover, an affecting version of Bob Dylan’s “To Make You Feel My Love” that slayed all others before or since. Loving the response to it, she wanted to do the same for her sophomore album, 21, released here last Tuesday. This time Adele has laid her stunning chops atop The Cure’s “Lovesong.”

In a Live On Letterman webcast last Monday night, Adele talked at length about the genesis of this particular cover-song selection. She didn’t originally set out to do the dark-tinged classic from 1989’s Disintegration, but rather the first song she ever learned how to play, INXS’ “Never Tear Us Apart”:

“I love Michael Hutchence, and that song is amazing… Anyway, I did it, and didn’t do a very good job. It was rubbish. I was listening back to it, and if I was INXS, I’d be gutted that I’d covered it.”

Back to square one, Adele brainstormed with her band in Malibu. Session guitarist Smokey Hormel suggested “Lovesong” by The Cure, recalling that Rick Rubin, one of 21‘s primary producers (and Adele’s Columbia Records boss), had at one point desired to do a bossa-nova covers record with Barbra Streisand. Hormel had worked on an arrangement of “Lovesong” for the project that never materialized.

Doing a tune intended for the Barbra Streisand? Adele couldn’t believe it. (“I know!” she told the Live On Letterman audience.) Upon hearing the bossa nova’d “Lovesong” for the first time, she also had quite an emotional reaction, as the UK singer was feeling quite homesick while holed up in a California recording studio:

“Smokey played this [arrangement] to me, and I grew up listening to The Cure, and I was missing my mum so much, and it was really weird becuase I had this kind of ‘Christmas Carol’ vision of my mum when I was six, and I could smell my apartment and everything. So I was truly moved by it, and so we covered it.”

Channeling her vividly personal connection to “Lovesong” in one take, the song landed 21‘s cover slot. Here’s Adele performing the song during her Live On Letterman set:

If, like me, you can’t get enough of Adele’s cover love, you can find her duet with Darius Rucker on Lady Antebellum’s “Need You Now” (taken from a CMT special last December) on the Target-exclusive deluxe version of 21. It’s one of four bonus tracks, along with live acoustic versions of “Someone Like You,” “Turning Tables,” and the countrified “Don’t You Remember” (a song inspired by “Need You Now” and early Dolly Parton).

And though Adele thinks her version of INXS’ “Never Tear Us Apart” was rubbish, I wouldn’t mind hearing her do it someday. Even at her worst (as if!), she’d definitely top this tragedy.

Purchase Adele – “Lovesong” via iTunes, Amazon MP3.