“Imaginary Friend” also begins detached and dry, its synth organ and tinny drum loop sounding almost desiccated. The track just gets jauntier as it develops: a twinkly piano, cartoon electro-buzz, and a verbose vocal that fills nearly all space in the arrangement. This all goes a long way to repress the longing for the unspecified but unrecoverable relationship with her titular “imaginary friend”; Kennedy’s vocal skips briskly through lyrics like “I got lost inside a world that isn’t real/And now it’s broken down,” as if bypassing their full implications. But seldom does longing stay properly repressed; a brief, languid instrumental break at the two-minute mark traces the wistful contours of that emotional world as it becomes harder and harder to access.

The album’s understated midpoint, “Feed Me,” is also its thematic center: “You squeeze everything out of me/Pop the air right out of my cheeks,” she sings in her softer mode against a disarmingly pleasant arrangement, making it sound romantic in a screwball kind of way—until the bridge turns the vocal into a shriek. And that shriek might seem to have settled the question of its meaning until Kennedy’s refrain: “Wouldn’t it be scary to realize it’s you who needs me?”

The song’s admission of vulnerability is strong enough to send the second half of the record hurtling back. Specifically, it hurtles backward through time, toward earnest Tin Pan Alley and Hollywood stylings. Kennedy has a low-key flair for these dramatics, and on Squeeze Me they leak out periodically—the string interlude in “Drive the Lorry,” the lurid, recurring Carla Dal Forno-esque tension in “Runner”—before the full proscenium curtain rises. But “Oakwood 21,” drowsy supper-club jazz complete with scatting, is the real deal. And the sumptuous dream-ballet instrumental of “Upstairs Cabaret” is in turn the surreal deal. She had Ennio Morricone in mind here, and matches his emotive swoon. This almost period-costumed detour into melodrama is captivating, all the more so considering how few of her art-pop peers attempt such a thing without poisoning it with irony or drugging it into a soporific drone. (One peer who has done it: Mitski, on her back-album tracks from Be the Cowboy.)

This section of the album is Kennedy at her most welcoming, but in a way that sounds either purposefully nostalgic (the fun-fair scene of “Closing Time”) or otherworldly. The moment must end, and so ends the reverie with “Hot Match,” which Kennedy called her first rock song. That may be a stretch—the pummeling Monsters closer “Dragged Myself Into the Sun” has a strong claim on that title, and “Feed Me” has fun with its classic-rock references, like a loping acoustic hook and drum breakdown that evoke “My Girl” and “In the Air Tonight” respectively. But on “Hot Match,” she fully commits to the bit, in her own way. She takes Chris Spedding’s 1975 hit “Motor Bikin’” and taps even deeper into its animating force of motorbikes rule, swapping out guitars for tire squeals as the steady motorik beat lets her maintain her poise. The song is admittedly a bit displaced on the record—there’s an alternate universe where this song is the massive single that gets tacked onto the end of the album. Still, no ending would better suit Squeeze Me than for Kennedy, after briefly having let listeners in, to coolly, collectedly drive away.