Infrastructure is crucial to the functioning of society and the economy. Yet, to avoid precipitating environmental breakdown, it must undergo transformation. We argue that citizens who rely on infrastructure's services should have a say in how transformation is managed. However, the complex nature of infrastructure means that public dialogue is difficult and rarely done well. Infrastructure has several characteristics, which make elicitation of perceptions challenging: it is connective, relational, obdurate, collective and subject to fragmented governance. We held a series of deliberative workshops in a city in the UK, to examine how public perceptions of infrastructure are shaped by these characteristics. We found that using infrastructure's characteristics as a framework for deliberation built participants' capabilities to articulate perceptions of infrastructure. We argue that using these characteristics also placed more emphasis on the socio-materiality of infrastructure and can address the disconnect between scales of participation and scales of decision making. This offers an alternative way to debate the desirable attributes of infrastructure, which we argue is more productive and inclusive.