Many industries are confronted by plateauing safety performance as measured by the absence of negative events – particularly lower-consequence incidents or injuries. At the same time, these industries are sometimes surprised by large fatal accidents that seem to have no connection with their understanding of the risks they faced; or with how they were measuring safety. This article reviews the safety literature to examine how both these surprises and the asymptote are linked to the very structures and practices organizations have in place to manage safety. The article finds that safety practices associated with compliance, control and quantification could be partly responsible. These can create a sense of invulnerability through safety performance close to zero; organizational resources can get deflected into unproductive or counterproductive initiatives; obsolete practices for keeping human performance within a pre-specified bandwidth are sustained; and accountability relationships can encourage suppression of the ‘bad news’ necessary to learn and improve.