Back in the days of vinyl records, when I felt like I had to have everything Genesis-related (but couldn't afford to buy it all), I briefly had the 12" single with the remixes of "Acting Very Strange" and "Couldn't Get Arrested."
At the time I had no idea that this remix of "Couldn't Get Arrested" was called the "Nix Mix" because it was "Nick's Mix." I assumed that it was called this because most of the lead vocal had been omitted (i.e., "nixed"). I even used this description later for a similar remix I heard elsewhere. And I still think it would be a good term for that kind of remix!