By signing an international river sharing agreement (RSA), countries voluntary commit to release water in exchange for a compensation. We examine the robustness of such commitments to reduced water flows. We focus on RSAs that satisfy core lower bounds and fairness upper bounds. We characterize the constrained upstream incremental RSA as the core and fair RSA that is sustainable during the most severe droughts. It assigns to each country its marginal contribution to its followers, up to its maximal benefit from water extraction. It lexicographically maximizes the welfare of the most upstream countries in the set of core and fair RSAs. Its mirror image, the downstream incremental RSA, is not sustainable to drought at the river source.