In 1984, Einsturzende Neubauten, with guests including Genesis P-Orridge, Stevo Pearce, Frank Tovey and others, played a show titled The Concerto for Voices and Machinery at the ICA in London. After 20 minutes the venue halted the show when the band began to dig through the venue's stage with drills and jackhammers.[2][3] 1984 also saw the first release of a best-of and rarities compilation, Strategies Against Architecture '80?'83.

The band's next album, Halber Mensch ("Half Man") in 1985,[1] may be seen as a developmental breakthrough. Musical structure became more evident, and Bargeld's lyrics and, especially, his singing changed. He moved from shouted words and phrases toward organized, poetic melodies.

The band played a show in Vancouver, Canada, to kick off its third North American tour. The performance was sponsored by the German Goethe Institute as part of the German contribution to Expo 86. Also scheduled to appear were Test Dept and Skinny Puppy, though not everyone was able to play.

On the tour, the group's experimental and improvised live performance style occasionally caused difficulties with venue management and law enforcement. A performance at The Palladium in Manhattan ended after an improvised pyrotechnics display. The band ignited lighter fluid in a couple of metal pans, and management stopped the performance and cleared the venue.[4][5]

The one-hour film Halber Mensch (1986) by S?go Ishii documents Einsturzende Neubauten's visit to Japan in 1985. The next two albums, Funf auf der nach oben offenen Richterskala ("Five on the open-ended Richterscale") in 1987[1] and Haus der Luge ("House of the Lie") in 1989,[1] were great successes in the United States and Japan.