In 1985, he signed to Steven Machat's label and production company, AMI. Machat, who was collaborating and working with a British producer, Richard James Burgess, hired Burgess to produce Abrams' self-titled debut album. Machat then arranged for MCA Records to sign Abrams for worldwide releases. Burgess produced the songs "Trapped", "I'm Not Gonna Let You", and "Table for Two".
"Trapped" reached the top five in the UK Singles Chart and topped the US Hot Dance Music/Club Play chart in 1985, followed by his self-titled album, which spent two weeks at number one the following year. An electronic remix of "Trapped" was later released in 1995 by Boards of Canada, under the pseudonym Hell Interface. A new version of "Trapped" ("Trapped 2006") was released in the UK.