The guitarist was consumed with his desire to pen a track as good as the famous song written by his Fab Four bandmate in the mid-1960s because so many fans mistakenly believed it was composed by Lennon.
When he came up with Imagine in 1971 he was convinced he finally had a tune to outdo MCCartney's masterpiece - and he pestered his Dj pal Howard Smith, demanding to know if it was better than Yesterday.
Smith tells Mojo magazine, "John came to my loft and he was all excited. He said, 'I think I finally wrote a song with as good a melody as Yesterday'. Yesterday drove him crazy. People'd say, 'Thank you for writing Yesterday, a beautiful song...' He was always civil, but it drove him nuts."
Lennon performed Imagine for Smith at his apartment and the depth of his obsession with beating MCCartney became clear.
Smith adds, "He played it through and asked me what I thought. (I said) 'It's beautiful.' (He said) 'But is it as good as Yesterday?' (I said) 'They're impossible to compare.' So he played it again. And again. And he said, 'You'll see, it's just as good as Yesterday.'"