For a little trivia, Johnette Napolitano (the voice of the band) worked for Leon Russell around the time of the band's inception. This probably explains the excellent cover of George Harrison's "Beware of Darkness" on Concrete Blonde's self-titled debut. Leon Russell sang the definitive version on Harrison's Concert for Bangladesh.
For hard-core Johnette fans, also check out the song "My Little Problem" on The Replacements record All Shook Down.
And for the band, stripped down 3 piece combo but achieved a fuller sound with Johnette's lush vocals and some nice guitar work.
Their self-titled debut seems to get critically panned but is very popular with fans. Its an excellent road trip album...with haunting lyrics draped over guitar work with just a touch of twang for the highway. The best example is True which forms a motif for the record, although it is more a collection of songs than a connected whole.