Most P2P systems divide a file into many pieces and fetch different pieces from many peers simultaneously. If one of the last few pieces is requested from an extremely slow peer, the overall download time may become excessive. The end-game mode was proposed to solve this problem. This method requests the last piece from all the connected peers at the same time. Unfortunately, the duplicated requests generate redundant traffic. This paper proposes a requesting method that does not increase overall download time as well as avoiding the redundant traffic. We also propose a combination of our requesting method and the end-game mode. The proposed methods are compared to the existing method with the end-game mode in simulations that use BitTorrent as a typical instance of the parallel retrieving P2P system. The results confirm that our requesting method can match the download times of the end-game mode while suppressing the redundant traffic. Our method enhances network performance by absorbing the difference in peer performance and providing steady download times without wasting traffic resources. Moreover, it is also confirmed that our combination method can distribute a file more quickly than other methods.