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Very preliminary, please do not quote without permission Abstract. This paper analyses Rawls’s celebrated difference principle, and a set of refinements of it, in societies with a finite and an infinite number of agents. A unified framework of analysis is set up, which al-lows one to characterise a family of egalitarian principles by means of a new axiom- the Harm Principle- recently proposed by [13]. This is quite surprising, because the Harm principle is meant to capture a liberal requirement of noninterference and it incorporates no obvious egalitarian content. A set of new characterisations of the maximin and of its lexicographic refinement are derived, including in the intergener-ational context with an infinite number of agents. Finally, a complete axiomatic characterisation of a new refinement of the difference princi-ple, recently proposed in the literature on intergenerational justice and environmental issues ([17], [20])- the recursive maximin- is provided