3D single object tracking (SOT) in LiDAR point clouds is a critical task in computer vision and autonomous driving. Despite great success having been achieved, the inherent sparsity of point clouds introduces a dual-redundancy challenge that limits existing trackers: (1) vast spatial redundancy from background noise impairs accuracy, and (2) informational redundancy within the foreground hinders efficiency. To tackle these issues, we propose CompTrack, a novel end-to-end framework that systematically eliminates both forms of redundancy in point clouds. First, CompTrack incorporates a Spatial Foreground Predictor (SFP) module to filter out irrelevant background noise based on information entropy, addressing spatial redundancy. Subsequently, its core is an Information Bottleneck-guided Dynamic Token Compression (IB-DTC) module that eliminates the informational redundancy within the foreground. Theoretically grounded in low-rank approximation, this module leverages an online SVD analysis to adaptively compress the redundant foreground into a compact and highly informative set of proxy tokens. Extensive experiments on KITTI, nuScenes and Waymo datasets demonstrate that CompTrack achieves top-performing tracking performance with superior efficiency, running at a real-time 90 FPS on a single RTX 3090 GPU.