The 'Wolves of Winter' rockers needed a song for their MTV Unplugged set at London's Roundhouse in November, and Simon - who is a long-time fan of the iconic rock band and co-founder Brian Wilson, and even has the song title tattooed on him as it was his first dance at his wedding - left his bandmates speechless when he came into the studio with the ''complex'' track figured out.
Speaking exclusively to BANG Showbiz, drummer Ben said: ''Simon did really well to work that one out.
''There were a few different covers in the pipeline and then one day he phoned up and said, 'I think I've got an idea, I'm going to go work on it.'
''I thought cool, he went away for one day and came in the next day and had it all worked out. Our jaws hit the floor.
''Some of the chord shapes are just so brutal and he was able to pull it off and sing one of the toughest songs around, so hats off to Mr. Simon Neil.''
The 38-year-old sticksman says he hopes Biffy can emulate the 'Good Vibrations' hitmakers' ability to produce ''accessible'' hits that are actually quite hard to play.
He said: ''The Beach Boys accomplished what we are also trying to accomplish.
''In terms of writing what are ultimately quite complex songs and making them sound like pop songs that are quite accessible.
''That is a real trick that only great bands can muster.''
Biffy head out on their 'MTV Unplugged' tour this September, including a date at London's iconic Royal Albert Hall on September 24.
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Brody Dalle's band dropped their first new music since 2003's 'Coral Fang'.
Sometimes actors are not acting.