This paper argues that human and material agents co-shape ‘morality’. Water systems will be discussed in more detail. Artefacts (technologies) relate humans and their worlds, but the specifics of this relationship become meaningful only within specific actor-networks. As such, the material influences the moral decisions of humans. Examples from the larger Mesopotamian area, on both state-led and community-managed water systems, are discussed to show that these result from activities of individuals, households and groups manipulating water fluxes in short time periods of hours and days. Analysis of these daily activities, and especially of how the material acts, offers options for archaeologists to trace morality in action.