"Mermaid Smiled" is a "jazzy" song inspired by a board book Partridge owned as a child. The title means "getting back in touch with the child in you. And the key to that is something as frivolous as a smile on a mermaid." It was composed in D6 tuning (D–A–D–A–B–F) and came about when he discovered a riff that he felt had an underwater quality to it. He wrote a poem containing some of the lyrics, called "Book Full of Sea", but could not remember if it was before or after he had the "Raga-mama-Raga" guitar motif: "I started to throw my hands around the fretboard and discovered some great-sounding stuff – all simple chords. They're just straight barres or real simple shapes. It just sort of said rock pools and mermaids and breakers crashing." Rundgren arranged the song in the style of Bobby Darin. The track features tabla, bongos, muted trumpets, and sampled vibraphones from a Fairlight; the latter two are reflected in the lyrics "from pools of xylophone clear" and "compose with trumpeting shell". Partridge found that the percussion gave the song an Indian feel and tried expanding upon it by singing flattened quarter notes, an idea that Rundgren rejected.