Conflicts between optimality and sustainability are typical in the literature on sustainable development. Using the 'capital-resource' growth model, Pezzey and Withagen (1998) have proved that if natural resources are exhaustible, the time-path of consumption is single-peaked, declining from some point in time onwards. This paper extends the model to include technical progress, resource renewability, extraction costs and population growth. The main result is that, for any constant returns to scale technology, optimal paths can be sustainable only if the social discount rate does not exceed the sum of the rates of resource regeneration and augmentation. The development of resource-saving techniques is crucial for sustaining consumption per capita in the long run, whereas capital depreciation and extraction costs are neutral with respect to this sustainability condition.