Public policy scholars have become increasingly concerned about a growing 'governance disconnect' - they see a growing fissure between the democratic politics of will formation and the messy, byzantine, networked, opaque world of public administration. Likewise, to the extent that deliberative system's theorists pay any attention to the complexities of real-world policy making processes, they tend to see them as pathologies or obstacles to be overcome. In this paper, we draw on a programme of research focused on a seemingly egregious example of the 'governance disconnect' in action - the work of quasi-independent, arms-length bodies in the British health sector. We show that these bodies can enable and house a range of administrative practices which foster novel forms of connection between public sites in civil society and empowered sites of policymaking. Some practices entail actors within arms-length bodies 'reaching out' to engage with civil society actors. Others entail civil society actors 'reaching in' to engage with and seek to alter the policymaking process. We dwell both on what enables these practices to emerge and flourish, and also what renders them limited or vulnerable in addressing the 'governance disconnect' in deliberative systems.