Originals: We're Not Supposed to Be Lovers by Adam Green (covered by Dean and Britta)
Adam Green's original of We're Not Supposed to be Lovers was released on his second solo album "friends of Mine" in 2003.
Dean & Britta's cover appeared on their Words You Used to Say EP in 2008
MP3: Dean & Britta - We're Not Supposed to be Lovers
Here's a live version recorded at a secret gig in Copenhagen in 2007:
And here's a sweet blurry video of that show