You must understand that these posts highlighting obscure Lennon And McCartney compositions are of historical interest, being some of the first songs they wrote and also, at the height of their early fame, it shows that they enthusiastically “churned them out”. In this case they might have churned out a somewhat inferior attempt, The Strangers with Mike Shannon being the first to agree to record and release the song after The Beatles themselves, Billy J. Kramer and The Fourmost had turned it down. It’s what might most commonly be known as – a turkey.
Best leave it to expert musicologist Ritchie Unterberger to tell the whole story on the All Music website:
“The Strangers with Mike Shannon (that is precisely how they were billed, not the other way around) had the honor, or misfortune, of covering the most obscure Lennon-McCartney song that was “given away” to another artist in the 1960s, and not recorded by the Beatles. This song was their May 1964 single “One and One Is Two,” and that did not chart in either the U.K. or the U.S. Of all the songs that fell into this category (with the possible exception of Carlos Mendes’ Paul McCartney-penned “Penina”), “One and One Is Two” was the most forgettable. A rather standard and plodding Merseybeat number without the melodic imagination that characterized even the weakest and most primitive songs the Beatles did on their first recordings, it attracted little notice at a time when Lennon-McCartney were the most in-demand composers in popular music.
Surprisingly little is known about the Strangers and Mike Shannon. Kristofer Engelhardt’s Beatles Undercover, which usually covers recordings that the Beatles contributed to as songwriters or performers in frighteningly intense detail, could only note that the group were probably from South Africa. The song itself, however, had a rather more complex history than simply popping up on the Strangers 45 and disappearing. The composition was apparently intended for use by Billy J. Kramer, who had already covered several Lennon-McCartney tunes for hits. It was written while the Beatleswere playing an extended engagement in Paris at the beginning of 1964, and a demo of McCartneysinging the song and accompanying himself on piano has been bootlegged. It has been reported that John Lennon said that if Kramer recorded the song, he (Kramer) would be finished. In his extensive interview for Playboy, the ever-gracious Lennon called it “another of Paul’s bad attempts at writing a song.”
The song was offered to Kramer, who decided not to record it. It was then offered to another Liverpool act that shared management with Brian Epstein, the Fourmost, who had already covered a couple ofLennon-McCartney songs that were not done by the Beatles for hit singles. They did give it a try but, as singer and lead guitarist Brian O’Hara remembered in Beatles Undercover, “McCartney came into the studio and played bass on “One and One Is Two,” but there just wasn’t any meat in the song and we couldn’t get anywhere with it.” Thus rejected by two artists (three if you count the Beatles, too), it made its way to the lowly Strangers with Mike Shannon. The single has proved difficult to find on reissue. It’s most likely to be found on the EMI compilation The Songs Lennon & McCartney Gave Away, which assembles 20 songs (all but one from the ’60s) that Lennon and McCartney wrote together or separately, and which the Beatles did not record for official release while they were together.”