So he called up an old college friend, Lou Reed, knowing that Reed, whose A Walk on the Walk Side features some of pop music's most famous "doo, doo, doos", would be good at it. It was a joke but Reed saw the funny side and didn't let him down.
Jeffreys has kept an address book full of famous names over the years, including Bruce Springsteen, Bob Marley and John Cale, and he tells a great story about being able to call in tenor saxophone colossus Sonny Rollins to play on his song Nothing Big in Sight on a late 1970s television show. His own name and music have often slipped under the radar or just not been promoted properly by record companies, however, because his lyrical observations on race – he's part African-American, part Puerto Rican – and other issues haven't sat well with those in positions of power in the music business.
There hass also been the question of how to market the music that this son of Brooklyn, New York, has been creating since he fell naturally into performing as a teenager in the early 1960s.
"I grew up listening to jazz," says Jeffreys, who makes his Scottish debut this weekend at a charity concert for Light of Day Scotland. "That's what my parents liked. My mum was young when she had me, she was still a teenybopper, and she and my dad would go out clubbing and dance to big bands. I can remember my mum dancing with me to a Count Basie record when I was about four. So I had Basie, Duke Ellington, Miles Davis, all those guys, in my background. Then I discovered music for myself, starting with Frankie Lymon. He was the same age as me – 12 – and I wanted to be him. Then along came Chuck Berry, rhythm 'n' blues, soul, folk music, pop, and all of that, and later reggae, too, found its way into what I do."
From the age of seven Jeffreys would take the train alone into central New York for his weekly piano lesson. As the father of a teenage girl, he shudders at the thought but remembers that times "weren't as insane" back then. He came to know Greenwich Village well, fell under the spell of singer-songwriters Fred Neil, Tim Hardin and presently, Bob Dylan, a major influence, and took up guitar, following his heroes in playing folk niteries such as Gerde's Folk City and the Gaslight.
His college friendship with Lou Reed never led to them forming a band, although Jeffreys did contribute guitar and a song, Fairweather Friend, to Reed's Velvet Underground colleague John Cale's Vintage Violence album in 1969. Around the same time, the band Jeffreys did form, the short-lived Grinder's Switch, which included pianist Stan Szelest, an associate of The Band, earned him his first recording contract.
Throughout the 1970s and into the 1980s Jeffreys released a series of critically acclaimed albums including Ghost Writer, which contained what's remained almost a theme song, Wild in the Streets. He wrote this after hearing about a pre-teen rape and murder in the Bronx and says the lesson to be learned from tackling subjects like this and other themes such as inter-racial romance and blatant racism (his song Don't Call Me Buckwheat actually resulted from the insult being hurled at him when he stood up at a baseball game) is to make your point with a good tune.
"That's the key," he says. "If you're going to say something important, you need to couch it in a strong melody, otherwise it'll sound too pedantic. Bob was the master of that, all these songs calling for social change and they became hits because of the easily remembered tune and the simple beat and chord changes."
Bob is, of course, Bob Marley, whom Jeffreys befriended when The Wailers were supporting another pal, Bruce Springsteen, at Max's Kansas City in 1972. Jeffreys's reggae connections remain strong and his next album is likely to find him working with another two old friends, reggae producer Dennis Bovell and dub poet Linton Kwesi Johnson.
He's still promoting The King of In Between, which was self-released after a gap of 13 years, due partly to his disillusionment with record companies and partly to a self-imposed break.
"When my daughter was born, I didn't want to be an absentee father, out on the road all the time," he says. "So I stayed home. Now she's 16 and an artist herself, I can go back to work. She writes great songs and sometimes she asks what I think of them and I try to tell the truth. But mostly, I stay out of it and d'you know what? Keeping quiet is the smartest thing I've ever done."
Garland Jeffreys plays Oran Mor, Glasgow, on November 23.