Complex sentence: The single was released in Canada and Japan, as a promo-only single in the U.S., and on the 2003 album, "The Essential Cyndi Lauper".
Split into simpler sentences: The single was released in Canada and Japan. In the U.S., Lauper released it as a promo-only single and more recently in 2003 on "The Essential Cyndi Lauper".