Simultaneous Localization and Mapping (SLAM) refers to the common requirement for autonomous platforms to estimate their pose and map their surroundings. There are many robust and real-time methods available for solving the SLAM problem. Most are divided into a front-end, which performs incremental pose estimation, and a back-end, which smooths and corrects the results. A low-drift front-end odometry solution is needed for robust and accurate back-end performance. Front-end methods employ various techniques, such as point cloud-to-point cloud (PC2PC) registration, key feature extraction and matching, and deep learning-based approaches. The front-end algorithms have become increasingly complex in the search for low-drift solutions and many now have large configuration parameter sets. It is desirable that the front-end algorithm should be inherently robust so that it does not need to be tuned by several, perhaps many, configuration parameters to achieve low drift in various environments. To address this issue, we propose Simple Mapping and Localization Estimation (SiMpLE), a front-end LiDAR-only odometry method that requires five low-sensitivity configurable parameters. SiMpLE is a scan-to-map point cloud registration algorithm that is straightforward to understand, configure, and implement. We evaluate SiMpLE using the KITTI, MulRan, UrbanNav, and a dataset created at the University of Queensland. SiMpLE performs among the top-ranked algorithms in the KITTI dataset and outperformed all prominent open-source approaches in the MulRan dataset whilst having the smallest configuration set. The UQ dataset also demonstrated accurate odometry with low-density point clouds using Velodyne VLP-16 and Livox Horizon LiDARs. SiMpLE is a front-end odometry solution that can be integrated with other sensing modalities and pose graph-based back-end methods for increased accuracy and long-term mapping. The lightweight and portable code for SiMpLE is available at: https://github.com/vb44/SiMpLE .