Moving-objects databases need a spatio-temporal indexing scheme for moving objects to efficiently process queries over continuously changing locations of the objects. A simple extension of the R-tree that employs time as the third dimension of the data universe shows low space utilization and poor search performance because of overlapping index regions. In this paper, we propose a variant of the 3-dimensional R-tree called the Adaptive 3DR-tree. The dynamic splitting policies of the Adaptive 3DR-tree significantly reduce the overlap rate, and this, in turn, results in improved query performance. The results of our extensive experiments show that the Adaptive 3DR-tree outperforms the original 3D R-tree and the TB-tree typically by a big margin.