The Single-Source Shortest Path (SSSP) problem is well-known for the challenges in developing fast, practical, and work-efficient parallel algorithms. This work introduces a novel shortest path search method. It allows paths with different lengths to be extended in parallel at the cost of almost negligible repeated relaxations. A dynamic-stepping heuristic is proposed for the method to efficiently reduce the extended paths and the synchronizations. A traversal-optimization heuristic is proposed to improve the method by efficiently reducing the created paths and alleviating the load imbalance. Based on the method, the two heuristics are used to develop a practical SSSP algorithm, which tactfully reduces workload and overhead. The heuristics and the algorithm were evaluated on 73 real-world and synthetic graphs. The algorithm was also compared with five state-of-the-art SSSP implementations. On each GAP benchmark suite graph except Road, its speedup to the best achieved by these five implementations is 2.5x to 5.83x.