Asylum seekers in Europe face increasingly restrictive policy regimes across the continent. In Denmark, they are held at designated asylum centres while their cases are processed and are subject to limitations on their movement, education and employment, as well as to a degree of surveillance from both the state and the Danish Red Cross, which operates the majority of the asylum centres. While these structures are in some ways reminiscent of Foucault's panopticon, I want to suggest a counterpoint to the panopticon, which I call the ‘myopticon’ to indicate the near-sightedness of the central surveying eye. The myopticon is a near-sighted system of surveillance practices, knowledges and sanctions, deployed as though it were panoptic. I want to suggest that the uncertainty that has soaked through the Danish asylum system and profoundly affected the asylum seekers in it is not a byproduct of bureaucratic processing, but intrinsic to the operation of the myopticon. By drawing out points of distinction with Foucault's panopticon, I sketch the outlines of a new technology of power that has powerful consequences for the daily lives of asylum seekers in Denmark.