The cloud computing paradigm offers many advantages over traditional self-hosting computing solutions by abstracting computations from infrastructure. An essential task for any cloud provider is task scheduling, wherein tasks are assigned to computing resources within the cloud system by a broker. Numerous cloud task scheduling algorithms exist including Min-Min, Max-Min, and Sufferage-though each is defined by performance trade-offs. BSufferage is proposed as a novel cloud task scheduling algorithm that augments the performance of the classical Sufferage algorithm. Modeling the algorithm using the open source CloudSim package and comparing it to its precursor yields performance results for BSufferage-demonstrating decreased completion times, increased throughput, and improved load balancing of resources.