As the band continued to rehearse, Dickson arranged a one-off single deal for the group with Elektra Records' founder Jac Holzman. The single, which coupled the band originals "Please Let Me Love You" and "Don't Be Long", featured McGuinn, Clark, and Crosby, augmented by session musicians Ray Pohlman on bass and Earl Palmer on drums. In an attempt to cash in on the British Invasion craze that was dominating the American charts at the time, the band's name was changed for the single release to the suitably British-sounding the Beefeaters. "Please Let Me Love You" was issued by Elektra Records on October 7, 1964, but it failed to chart.
In August 1964, Dickson managed to acquire an acetate disc of the then-unreleased Bob Dylan song "Mr. Tambourine Man", which he felt would make an effective cover for the Jet Set. Although the band was initially unimpressed with the song, they began rehearsing it with a rock band arrangement, changing the time signature from 2/4 to a rockier 4/4 configuration in the process. In an attempt to bolster the group's confidence in the song, Dickson invited Dylan himself to World Pacific to hear the band perform "Mr. Tambourine Man". Impressed by the group's rendition, Dylan enthusiastically commented, "Wow, man! You can dance to that!" His ringing endorsement erased any lingering doubts that the band had over the song's suitability.