Load sharing algorithms can use sender-initiated, receiver-initiated, or symmetrically-initiated schemes to improve performance in distributed systems. The relative performance of these schemes has been shown to depend on the system load. The author proposes an adaptive symmetrically-initiated scheme where all nodes alternate between a sender-initiated and a receiver-initiated algorithm depending on the current system load. Simulations show that the mean job response times for the proposed scheme are superior to the best attained by its two algorithms used separately and simultaneously. The alternating scheme performs best at intermediate and high loads, when the job arrival process is bursty, and when it is costly to find complementary nodes.