This article describes the background to a pilot project with formative peer feedback on a graded essay in a major compulsory undergraduate course. Peer feedback was implemented mainly as a response to a need on the part of the students for more feedback. We discuss the theory behind peer feedback as a teaching method and the realization of the project, including the process behind the design of criteria for the peer feedback. Through interviews with some of the students involved and through the students' questions in the process, we gained insight into how the students perceived the peer feedback process, what worked for them and what challenges arose. The post-processing focused particularly on the usefulness, for both teachers and students, of clarifying criteria for such a task.