Recent natural resource discoveries in East Africa provide an enormous opportunity for development. We focus on oil discoveries in Uganda and their expected impact on government revenues. We analyze alternative spending policies of natural resource revenues using a calibrated dynamic, stochastic, general equilibrium model (DSGE). We use detailed publicly-available information on the upstream oil sector and the fiscal regime to derive realistic cost and government revenue profiles across a range of oil price scenarios. This enables us to project annual production, fixed and variable costs, and government revenues for given global oil price paths. We compare the potential effects of income transfers versus public investment spending, as well as front-loaded versus gradual public investment policies. We also assess the impacts of alternative assumptions on the efficiency of public investment due to constraints on absorptive capacity. In terms of economic welfare, income transfers dominate public investments (whether gradual or front-loaded) given the typically low discount factors for households in low-income developing countries. Similarly, front-loaded investment policies dominate gradual investment policies given the low discount factors. However, our simulations show that as individuals care more about the future (i.e. have a lower discount rate), the welfare order of policies change, as the productivity effect of public investment produces a higher increase in consumption and welfare even though this increase is lagged in time.