Informal settlement is a form of incremental urban design and planning that seems set to remain a primary mode of urban development in cities of the global South. Yet, we know very little about how incremental urbanism works. In this paper, we suggest a typology of increments as a conceptual lens for understanding the emergence of informal settlement morphologies. We consider the ways residents extend and renovate buildings at micro-spatial scales and identify typical increments of 'extend', 'attach', 'replace', 'divide', 'connect' and 'infill'. We also explore the informal rights and codes that govern the ways in which some increments encroach on public space – ‘rights of way’, ‘air-rights’ and ‘the right to light and ventilation’. We enga...