In this paper we explore scheduling and runtime system support for unordered distributed graph computations that rely on optimistic (speculative) execution. Performance of such algorithms is impacted by two competing trends: the higher degree of parallelism enabled by optimistic execution in turn requires substantial runtime support. To address the potentially high overhead and scheduling complexity introduced by the runtime, we investigate customizable scheduling policies that augment the scheduler of the underlying runtime to adapt it to a specific graph application. We present several implementations of Distributed Control (DC), a data-driven unordered approach with work prioritization and demonstrate that customizable scheduling policies result in the most efficient implementation, outperforming the well-known ?-stepping Single-Source Shortest Paths (SSSP) and Jones-Plassmann vertex-coloring algorithms. We apply two scheduling techniques, flow control and adaptive frequency of network progress, which allow application-level control over the balance of domain work and the runtime work. Experimental results show the benefit of such application-aware scheduling for irregular distributed graph algorithms.