In a statement, Costello called "Come for Me" the New Years Day version of Gwen Stefani's "Hollaback Girl
," if it were "A LOT heavier."
However, the song Costello played to the track's producers, Scott Stevens and Mitchell Marlow, was another Stefani-sung tune: No Doubt's "Hella Good." Speaking to the British magazine Rock Sound
, she explained that she told her collaborators she loves the way "Hella Good"'s structure is based on one riff on repeat for the entire song. "That's how 'Come For Me' started," Costello added. "The guitar riff intro is the same guitar riff in the chorus, and that's what started getting the songwriting process going for that. I love its simplicity and its catchiness."