This paper describes a new approach to the problem of resolving distributional conflicts between generations. We impose conditions on the social preferences capturing the following idea: If indifference or preference holds between truncated paths for infinitely many truncating times, then indifference or preference holds also between the untruncated infinite paths. Within this framework, we show (1) how such a condition provides an improved solution to the problem of combining Strong Pareto and impartiality in an intergenerational setting, and (2) how equity conditions well-known from the finite setting can be used to characterize different versions of leximin and utilitarianism.