The album includes covers of the Arthur Hamilton standard "Cry Me a River", as well as "Magnolia", an early song of J. J. Cale's.

"I Believe", which was a moderate hit in the United States, was included in a special song collection compact disc sold around the same time by fashion retailer Banana Republic.

The Allmusic review by Stephen Thomas Erlewine awarded the album four out of five stars, describing it as "a stylish amalgam of jazzy sophisti-pop, Motown, swinging '60s rock, trip hop and contemporary soul.

That voice – along with songs that show how powerful his updated blue-eyed soul can be, like "I Believe" and "Don't Give Me Away" — is what makes Heaven such a promising and successful debut.

"[4] A couple of months following its release, Heaven made a brief appearance on the Billboard Heatseekers Album Chart during the week of 31 January 1998, where it ranked at number 49.