Theoretically, the Multiple Hypothesis Tracking (MHT) method is the most powerful approach for tracking multiple targets. The MHT method, however, leads to combinatorial explosion and computational overload. By using an algorithm for finding the K-best assignments, the MHT approach can be considerably optimized in terms of computational load. A much simpler alternative of the MHT approach is provided by the Joint Probabilistic Data Association (JPDA) algorithm in combination with the Interacting Multiple Models (IMM) approach. Even though it is much more simple, this approach can also be computationally overwhelming. To overcome this drawback, an algorithm due to Murty and optimized by Miller, Stone and Cox is embedded in the IMM-JPDA algorithm in order to determine a ranked set of K-best hypotheses (instead of all feasible hypotheses). The presented algorithm assures continuous maneuver detection and adequate estimation of maneuvering targets in heavy clutter. This results in a good overall target tracking performance with moderate computational and memory requirements. The article further presents corresponding simulation results.