This paper argues that it is time for public understanding of science to develop a critical inventory of the forms, formats and methods of public participation and their respective implications and ambiguities. It highlights the need for analysing not only the limitations and deficiencies of participatory arrangements but also their constructive dimension, in particular the construction of the subject of participation. Looking into participatory governance arrangements in the issue area of genetic testing in Germany and the UK the paper presents a typology of formats according to the way the respective public is constructed and identifies four major constructions of publics: the general public, the pure public, the affected public and the partisan public. Each of these enables certain speaking positions while foreclosing others. The study shows that the main purposes of participatory arrangements in this issue area are knowledge production and education rather than political deliberation and decision-making.