Mapping global vertical vegetation structure (VS) is critical for the quantification of global carbon stocks. While orbital LIDAR measurements of NASA’s Global Ecosystem Dynamics Investigation (GEDI) mission provide direct estimates of vertical VS, they only cover 4% of the global land surface. Recent works have produced global contiguous maps of canopy height using convolutional neural network (CNN) models and satellite imagery. However, these models faced some challenges estimating high canopy heights (>30 m) and identified some tiling artifacts (Lang et al., 2022; Potapov et al., 2020).We present various methods to address these limitations. First, we remove tiling artifacts by using overlapping tiles when producing maps and removing zero-padding from CNN architectures. Second, we compare the benefits and limitations of a few different methods to improve high canopy height estimation. Among the methods is histogram matching predicted heights to nearby LIDAR measurements. Another is learning a calibration model to correct each pixel based on similar known measurements nearby. Finally, we borrow recent advances in deep depth completion from the autonomous driving field to create an integrated model that uses known values to improve the prediction map. To demonstrate these methods, we map global vertical VS with a CNN model at 1km resolution using observations from Landsat, L-band synthetic aperture radar observations from the Advanced Land Observing Satellite (ALOS) PALSAR-2, and surface topography. For model training, GEDI relative height metrics are filtered and aggregated into 1km grids. We also use measurements from the Ice, Cloud and land Elevation Satellite 2 (ICESat-2), inter-calibrated with GEDI using co-located measurements. Finally, we apply the aforementioned corrective methods to the product, reporting global RMSE and MAE metrics, as well as visual qualitative observations. These results open the path for unsaturated global vertical VS products at higher 500 m, 200 m, and 100 m resolutions.