In descriptions of a just transition to a sustainable future, ensuring a decent quality of life whilst remaining within planetary boundaries are often dual central aims. However, at present no country is moving in the right direction at the necessary speed to achieve this. In response, the need to reduce socio-economic inequality is increasingly highlighted in climate mitigation proposals, spanning a broad range of economic narratives of climate change mitigation, including Green Growth, Green New Deal, Post-Growth and Degrowth proposals. Despite broad support within sustainability transition literature for inequality reduction, the relationship between inequality and planetary boundaries is complex and understudied, particularly with regards to the climate impact economic inequality reduction may have in these divergent economic policy narratives. Through a structured integrative review of the academic literature that discusses inequality reduction alongside these narratives, this paper unpicks the motivations for and mechanisms through which socio-economic inequality reduction may be achieved. Whilst the narratives share the goal of achieving inequality reduction, the purposes for, mechanisms through which inequality reduction is to be achieved, and conviction through which inequality reduction is pursued is often distinct. It is argued that these differences may result in divergent climate impacts of ensuring decent living standards under each economic future. Despite this potential, none of the narratives offer investigation to these impacts, indicating the need for further empirical investigation of this important tension in climate change mitigation research.