I will present a construction of vacua of string theory in which the magnitude of the cosmological constant is exponentially small. The vacua are supersymmetric AdS solutions in flux compactifications of type IIB string theory, with all moduli stabilized. The vacuum energy is small because we ensure the exact cancellation of all perturbative contributions, through an explicit choice of integer parameters determined by the topology and quantized fluxes. The nonperturbative contributions that remain are exponential in these integers. Finding cosmological constants of small magnitude in this landscape is exponentially easier than in Bousso-Polchinski landscapes, but extending our approach to positive cosmological constants in realistic universes is a difficult open problem.