Natural resource revenues are an increasingly important financing source for public investment in many developing economies. Investing volatile resource revenues, however, may subject an economy to macroeconomic instability. This paper applies to Angola the fiscal framework developed in Berg et al. (forthcoming) that incorporates investment inefficiency and absorptive capacity constraints, often encountered in developing countries. The sustainable investing approach, which combines a stable fiscal regime with external savings, can convert resource wealth to development gains while maintaining economic stability. Stochastic simulations demonstrate how the framework can be used to inform allocations between capital spending and external savings when facing uncertain oil revenues. An overly aggressive investment scaling-up path could result in insufficient fiscal buffers when faced with negative oil price shocks. Consequently, investment progress can be interrupted, driving up the capital depreciation rate, undermining economic stability, and lowering the growth benefits of public investment.