Arguably the Greatest Singles Band in America, the Mavericks have earned considerably less respect than they deserve in the United States, a problem, I’m afraid, rooted firmly in their strengths. Of course you know about the Latin influence (that’s too weak a word) on their songs, the horns and beats that turn the new “Here Comes My Baby” into the most infectiously joyous thing you’ve heard in years. And you certainly know that Raul Malo is one of America’s finest vocalists, a singer whose range, both musically and emotionally, make comparisons with Van Morrison’s or Ray Charles’ greatness viable.

But the strengths which seem most to have put off the American public are more rooted in country music’s current identity problem, its obsessive drive to insist on its own importance. (Cf., by the way, Nascar fans’ insistence that their favorite drivers are really, REALLY, athletes). So country music aims for an audience of first-gen suburban families who yearn for sophistication and reject signs that might prove that grandpa never took much to school-learning, but knew enough to build a decent life for his wife and babies.

Therefore you will not hear too much of the pedal steel and low-note twanginess of this or other Mavericks CDs roaring out of the speakers of SUVs idling at red lights near the mall; think of the wise-ass looks you’d get from teenagers with their hats on backwards, you’d best stick with Shania. And the pure cornball pleasure the band takes in echoing the slick pop of the fifties and sixties (one of their album’s titles, Music for All Occasions, seems to have been stolen from some lost lounge singer masterwork) surely tests the resolve of listeners too self-conscious to have a good time.

But try this one. From beginning to end—or, since it’s in reverse chronological order, end to beginning—it reveals a band as willing as any in recent history to explore the places where genre breaks down and all that is left is great music.