The continuous depletion of nonrenewable natural resources and climate change may lead to a future characterized by a higher frequency of extreme natural events (i.e., flooding, hurricanes, and droughts) and resource supply shocks (i.e., oil price shock). Sub-Saharan African countries will be particularly exposed to these types of shock due to their socioeconomic conditions and geographical conformation. This study investigates the impact of two contemporaneous covariant sudden shocks (i.e., drought and price oil shock) and the possible coping strategies through a static computable general equilibrium (CGE) model for Kenya. The results suggest that a mitigation policy as public transfers is an effective mitigation tool for drought effects, improving welfare and GDP in the short run. However, adopting public transfers during an oil crisis may have regressive effects on population income and welfare. Because the mitigation effectiveness is strongly affected by the complex interaction of combined shocks, the public authorities should pay attention to policy implementation. These findings call for a new scheme of transfer allocation where rural and low-income household quantiles should receive more attention by postdrought mitigation policy, being that they are more vulnerable to external shocks.