LiDAR is a promising tool for fast and accurate measurements of trees. There are several approaches to estimate aboveground woody biomass using LiDAR point clouds. One of the most widely used method consists in fitting geometric primitives (e.g. cylinders) to the point cloud, thereby reconstructing both the geometry and topology of the tree. However, current algorithms are not suited for accurate estimation of the biomass of finer branches, because of the unreliable point dispersions from the movements induced by wind, occlusion in the upper canopy, or the relatively large laser footprint compared to the structure diameter. We propose a new method that couples point cloud-based reconstructions and structural models to estimate accurately the aboveground woody biomass of trees, including finer branches. The model was trained using branch samples from the trees, and accurately predicted the biomass with 1.6% nRMSE at the segment scale from a k-fold cross-validation. It also gave satisfactory results when up-scaled to the branch level with a significantly lower error (13% nRMSE) and bias (-5%) compared to fitting cylinders to the point cloud (nRMSE: 92%), or using the pipe model theory (nRMSE: 31%). The model was then applied to the whole-tree scale, and showed that the sampled trees had more than 1.7km of structures in average, and that 96% of that length was coming from the twigs (i.e. <5 cm diameter). Our results showed that neglecting twigs lead to a significant underestimation of tree aboveground woody biomass (-21%) in our study case. The structural model approach is promising for unbiased large-scale estimations, and could be used as a new way for accurate estimation of the standing biomass without the need for tree cutting.