We give an overview of confidentiality approaches based on random noise that are currently discussed for population statistics and censuses. We remark on utility and risk aspects of some specific output mechanisms, focusing on static outputs that are typical in population statistics. It is argued that unbounded noise distributions, such as strictly differentially private ones, jeopardise unique census features without a clear need. Finally, typical attacks are analysed to constrain generic noise parameters to a good risk/utility compromise for the 2021 EU census scenario. The analysis also shows that strictly differentially private mechanisms would be severely constrained in this scenario.