Automation of forest field reference data collection has been an intensive research objective for laser scanning scientists ever since the invention of terrestrial laser scanning more than two decades ago. Recently, it has been proposed that such automated data collection providing both the tree heights and stem curves would require a combination of above-canopy UAV point clouds and terrestrial point clouds. In this study, we demonstrate that an under-canopy UAV laser scanning system utilizing a rotating laser scanner can alone provide accurate estimates of the canopy height and the stem volume for the majority of the trees in a boreal forest. To this end, we mounted a rotating laser scanner based on a Velodyne VLP-16 sensor onboard a manually piloted UAV. The UAV was commanded with the help of a live video feed from the onboard camera of the UAV. Since the system was based on a rotating laser scanner providing varying view angles, all important elements such as treetops, branches, trunks, and ground could be recorded with laser hits. In an experiment including two different forest structures, namely sparse and obstructed canopy, we showed that our system can measure the heights of individual trees with a bias of -20 cm and a standard error of 40 cm in the sparse forest and with a bias of -65 cm and a standard error of 1 m in the obstructed forest. The accuracy of the obtained tree height estimates was equivalent to airborne above-canopy UAV surveys conducted in similar forest conditions. The higher underestimation and higher inaccuracy in the obstructed site can be attributed to three trees with a height exceeding 25 m and the applied laser scanning system VLP-16 that had a limited height measurement capacity when it comes to trees taller than 25 m. Additionally, we used our system to estimate the stem volumes of individual trees with a standard error at the level of 10%. This level of error is equivalent to the error obtained when merging above-canopy UAV laser scanner data with terrestrial point cloud data. Future research is needed for testing new sensors, for implementing autonomous operation inside canopies through collision avoidance and navigation through canopies, and for developing robust methods that work also with more complex forest structure. The results show that we do not necessarily need a combination of terrestrial point clouds and point clouds collected using above-canopy UAV systems in order to accurately estimate the heights and the volumes of individual trees.