Patient and Pareto responsive (pPr) societal preferences were introduced and studied in Khan and Stinchcombe (2018). This paper develops a tractable subclass of the pPr preferences that satisfy a strong equity criterion formulated to match intuitions and results for large but finite models. In population models where the number and happiness of future people is stochastic, the only optimal policies require sustainability (resp. an abundance of effort) in the presence of irreversible (resp. difficult to reverse) negative externalities suffered by future generations. Partially ordering the preferences by increasing degrees of inequality aversion over generations, more inequality averse preferences give rise to choices that are counterintutive from population ethics viewpoint in smaller sets of problems.