The paper addresses issues of scientific conduct regarding relations between science and the media, relations between scientists and journalists, and attitudes towards the public at large. In the large and increasing body of literature on scientific conduct and misconduct, these issues seem underexposed as ethical challenges. Consequently, individual scientists here tend to be left alone with problems and dilemmas, with no guidance for good conduct. Ideas are presented about how to make up for this omission. Using a practical, ethical approach, the paper attempts to identify ways scientists might deal with ethical public relations issues, guided by a norm or maxim of openness. Drawing on and rethinking the CUDOS codification of the scientific ethos, as it was worked out by Robert K. Merton in 1942, we propose that this, which is echoed in current codifications of norms for good scientific conduct, contains a tacit maxim of openness which may naturally be extended to cover the public relations of science. Discussing openness as access, accountability, transparency and receptiveness, the argumentation concentrates on the possible prevention of misconduct with respect to, on the one hand, sins of omission—withholding important information from the public—and, on the other hand, abuses of the authority of science in order to gain publicity. Statements from interviews with scientists are used to illustrate how scientists might view the relevance of the issues raised.