The scientific investigation of forest ecosystems requires precise information on the three-dimensional structure of trees. Full-waveform airborne laser scanner data contain very valuable information on the biophysical structure in forest stands. Beyond 3D point cloud representations obtained from full-waveform decomposition techniques, volumetric representations of full-waveform laser scanner data (i.e. 3D voxel spaces) form a valuable basis for various scientific analysis ranging from biomass determination (or biomass change determination) over habitat analysis to meteorological gas exchange investigations. In order to achieve volumetric forest stand representations of high geometric and radiometric quality, the raw measurement data have to be prepared for the transformation into the voxel structure. The preparation of the full-waveform airborne laser scanner data comprises on the one hand the reconstruction of the differential backscatter cross section. On the other hand, we have to apply a radiometric correction on the reconstructed differential backscatter cross section, since each individual laser pulse echo is significantly affected by attenuation effects caused by partial reflections in higher regions of the crown during the laser pulse propagation through the vegetation. As a result, the structure in the lower parts of the vegetation is underrepresented in the digitized waveform and consequently also in the volumetric reconstruction. In this paper, we present novel methods for the radiometric enhancement of full-waveform airborne laser scanner data for volumetric representations in environmental applications. Our approach allows the numerically stable reconstruction of the effective differential backscatter cross section using appropriate deconvolution and regularization techniques. Moreover, we developed a correction method, which compensates for the loss of signal strength caused by partial reflections on the path of a laser pulse through the canopy. The correction term is derived from the differential backscatter cross section directly via a waveform history analysis. The basic idea of the correction method is a stepwise increase of the signal amplitudes depending on the individual history of each laser pulse. Therefore, the procedure is also referred to as pulse history correction. Our novel methods contribute to an improved access to the information on vegetation structure contained in full-waveform laser scanner data. Furthermore, they allow to overcome limitations of existing approaches, which are mainly based on the extraction of discrete maxima.