The song dealt with Bowie’s feelings for his schizophrenic half-brother Terry, who had committed suicide on 16 January 1985. The lyrics tell of a man pushed to utter desperation by the pressure put on him. Bowie has also cited his own feelings about jumping into the unknown metaphysically. Musically, the influence of Nile Rodgers led to a funk-based sound, though the track was also influenced by contemporary jazz, with a solo from avant-jazz trumpeter Lester Bowie.

As the lead-off single, "Jump They Say" received a considerable promotional push from Bowie’s new label, Savage Records (though Arista Records distributed the package in Europe). A striking video was shot by Mark Romanek, depicting Bowie as a businessman paranoid of his colleagues, who seemingly conduct experiments on him and find him a disturbing influence, forcing him to jump from the roof of the corporate building to his death. The video is heavily influenced by Jean-Luc Godard's 1965 film Alphaville, as well as Chris Marker's film La jetée and Orson Welles' The Trial - both from 1962. The uniformed women shown monitoring Bowie through high powered telescopes are an homage to the stewardesses in the Pan-Am space plane in Stanley Kubrick's 1968 epic 2001: A Space Odyssey. The song, while not Bowie’s first release since Tin Machine, was pushed as a comeback single, and reached No. 9 in the UK charts – Bowie’s only top 10 single between 1986's "Absolute Beginners" and 2013's "Where Are We Now?"

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