In this paper we reflect on the process of co-design by detailing and comparing two strategies for the participatory development of interaction concepts and prototypes in the context of technologically-enhanced museum visiting experiences. While much work in CSCW, HCI and related disciplines has examined different role configurations in codesign, more research is needed on examining how collaborative design processes can unfold in different ways. Here we present two instances of co-design of museum visiting aids, one stemming from an open brief, another from an initial working prototype; we discuss the process in each case and discuss how these alternative strategies presented the team with different possibilities as well as constraints, and led to different patterns of collaboration within the design team. Finally, we draw a set of themes for discussion and reflection to inform and aid researchers and practitioners participating in similar co-design processes, particularly in the domain of cultural heritage.