[3] It features string arrangements by Vince Mendoza, who, along with producer Larry Klein, is known for his works with Joni Mitchell.

[4] A deluxe edition was released in November 2009, which consists of a digipak including an orchestral version of "If the Stars Were Mine" and an additional EP with five tracks recorded live at a radio concert in Paris, as well as an extended booklet.

[6] Keeping the dark piano jazz style, the album incorporates several elements of samba and Brazilian music, which Gardot considers major influences.

[12] Ian Patterson writing for All About Jazz added, "Gardot blurs the line between the beauty and pain of loving; hope and hopelessness are thinly disguised mirror images, and romance can be something as elusive as mist, but yet something powerful and all consuming.

"[9] Michael Quinn of BBC commented, "My One and Only Thrill is the spellbinding follow up to Gardot's compelling debut, Worrisome Heart, and eloquently confirms her as a supreme songwriting talent possessed of a truly sublime voice.

"[15] Will Layman of PopMatters observed, "Melody Gardot is singer with a great sound -- intimate rather than overblown, tinged with smoke rather than hype, a retro-ish kind of now.