With the rapid development of wireless communication and mobile equipment, many applications for location-based services have been emerging. Moving objects such as vehicles and ships change their positions over time. Moving objects have their moving path, called the trajectory, because they move continuously. To monitor the trajectory of moving objects in a large scale database system, an efficient Indexing scheme to processed queries related to trajectories is required. In this paper, we focus on the issues of minimizing the dead space of index structures. The Minimum Bounding Boxes (MBBs) of non-leaf nodes in trajectory-preserving indexing schemes have large amounts of dead space since trajectory preservation is achieved at the sacrifice of the spatial locality of trajectories. In this thesis, we propose entry relocating techniques to reduce dead space and overlaps in non-leaf nodes. we present performance studies that compare the proposed index schemes with the TB-tree and the R*-tree under a varying set of spatio-temporal queries.