During 1979, the band began to attract a live following in London, being regulars at the Dublin Castle in Camden Town. The band's first commercial recording was the Lee Thompson composition "The Prince". The song, like the band's name, paid homage to their idol, Prince Buster. The song was released through 2 Tone Records, the label of The Specials founder Jerry Dammers. The song was a surprise hit, peaking in the UK music charts at number 16. A performance of "The Prince" on popular UK music show Top of the Pops helped Madness gain public recognition. Madness then toured with fellow 2 Tone bands The Specials and The Selecter, before recording their debut album.  That debut album, One Step Beyond... was released by Stiff Records. The album included a re-recording of "The Prince" and its B-side "Madness", and the band's second and third singles: "One Step Beyond" and "My Girl". The title song was a cover of the B-side of the 1960s Prince Buster hit "Al Capone". One Step Beyond... stayed in the British charts for 78 weeks, peaking at number 2. After the release of "My Girl", the band felt that they had exhausted the material from One Step Beyond..., and did not want to release any more singles from the album. However, Dave Robinson, head of Stiff Records, disagreed. Eventually, a compromise was made, and the band decided to release an EP featuring one album track and three new tracks. The result was the Work Rest and Play EP, which was headlined by the song "Night Boat to Cairo", from the One Step Beyond album. The EP reached number 6 in the UK singles chart.  Live recordings of Madness performances as well as those by other 2 Tone bands were used in the documentary film and soundtrack album Dance Craze.  In 1980, the band's second album, Absolutely reached number 2 in the UK album charts. Absolutely spawned some of the band's biggest hits, most notably "Baggy Trousers", which peaked at number 3 in the UK singles chart. "Embarrassment" reached number 4 in the charts, and the instrumental song "The Return of the Los Palmas 7" climbed to number 7. Although the album reviews were generally less enthusiastic than those of One Step Beyond..., they were mostly positive. Robert Christgau gave the album a favourable B- grade, but Rolling Stone awarded the album just one out of five stars. Rolling Stone was particularly scathing of the ska revival in general, stating that "The Specials wasn't very good" and Madness were simply "the Blues Brothers with English accents".  A drama-documentary film entitled Take It or Leave It was released in 1981, featuring the band members playing themselves in a re-creation of their early days to the then-current period.

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