Traffic jams often occur without any obvious reasons such as traffic accidents, roadwork, or closed lanes. Under moderate to high traffic density, minor perturbations to traffic flow (e.g., a strong braking motion) are easily amplified into a wave of stop-and-go traffic. This is known as a phantom jam. In this paper, we aim to mitigate phantom jams leveraging the three-phase traffic theory and vehicle-to-vehicle (V2V) communication. More specifically, an efficient phantom jam control protocol is proposed in which a fuzzy inference system is integrated with a V2V-based phantom jam detection algorithm to effectively capture the dynamics of traffic jams. Per-lane speed difference under traffic congestion is taken into account in the protocol design, so that a phantom jam is controlled separately for each lane, improving the performance of the proposed protocol. We implemented the protocol in the Jist/SWAN traffic simulator. Simulations with artificially generated traffic data and real-world traffic data collected from vehicle loop detectors on Interstate 880, California, USA, demonstrate that our approach has by up to 9% and 4.9% smaller average travel times (at penetration rates of 10%) compared with a state-of-the-art approach, respectively.