Uspavanka za Radmilu M. was Bijelo Dugme's last studio album recorded with vocalist Željko Bebek. Uspavanka za Radmilu M. is the band's first album since the 1977 live album Koncert kod Hajdučke česme to feature drummer Ipe Ivandić and the first one since the 1975 album Šta bi dao da si na mom mjestu to be recorded in the band's default lineup.

The band's leader, guitarist Goran Bregović, originally intended to release Uspavanka za Radmilu M. as Bijelo Dugme's farewell album and to dismiss the band after the promotional tour. Unlike the band's previous albums, Uspavanka za Radmilu M. was not followed by a large promotion in the media.

The album was recorded in Skopje. Uspavanka za Radmilu M. was the band's first album since the 1977 live album Koncert kod Hajdučke česme to feature drummer Ipe Ivandić, who returned to the band at the end of 1982, replacing Garabet Tavitjan, who performed with the band only on the 1982 Bulgarian tour. The album was produced by Bregović and Gajo Vučićević and featured Leb i Sol member Vlatko Stefanovski (guitar), Blagoje Morotov (double bass) and Arsen Ereš (saxophone) as guest musicians. It was mixed in Britannia Row Studios in London. The songs "Ako možeš zaboravi", "U vrijeme otkazanih letova", "Polubauk polukruži poluevropom" (trans. "Half-Spectre Is Half-Haunting Half-Europe", the title referring to the first sentence of The Communist Manifesto) and "Ovaj ples dame biraju" featured diverse sound, illustrating various phases in the band's career. The album's title track is the only instrumental track Bijelo Dugme ever recorded.

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