We proposed a new area-based approach to process Lidar point clouds and develop new sets of metrics to improve models dedicated to predict forest parameters. First, we introduced point normalization based on penetration depth below the outer canopy layer to avoid biases introduced by ground normalization and canopy surface heterogeneity during metric computation. Second, we proposed computation of area and volume metrics from canopy surface models computed from both first and last returns to better characterize the 3D plot heterogeneity. The set of proposed metrics were combined with traditional ones, based on point height above ground level, to measure their contribution to models of basal area (BA) and aboveground volume (AGV). The modeling framework included a wide range of forest types, canopy structures and Lidar characteristics. Models were developed for all sites grouped together or separately. In each case, the set of metrics was submitted to a hierarchical clustering process to select the best variables to be included in the models that were further established using a best-subset method. Overall, the introduction of the proposed metrics allowed a reduction in models root mean squared error from - 0.06% to 19.58% according to forest types and target forest parameters. Best improvements were achieved for broadleaved forests, showing the potential of the proposed metrics to efficiently characterize the structure of such porous forest canopies.