Density heterogeneities in the path of proton beams are known to cause degradation of the Bragg peak and, thus, widening of its distal fall-off. Inadequate accounting for this effect may lead to unwanted dose delivered to normal tissue distal to the target volume. In low-density regions, such as the thorax, this may lead to large volumes of healthy tissue receiving unnecessary dose. Although it is known that multiple Coulomb scattering within the density heterogeneities is the main cause of Bragg peak degradation, no systematic attempt has been made to quantify the contribution of multiple Coulomb scattering and nuclear scattering. Through a systematic study using a 220 MeV proton beam, we show that nuclear scattering contributes to about 5% of the distal fall-off width and is only slightly dependent on heterogeneity complexity. Furthermore, we also show that the energy spectra of the proton fluence downstream of various heterogeneity volumes are well correlated with the Bragg peak distal fall-off widths. Based on this correlation, a novel method for predicting distal fall-offs is suggested. This method is tested for three clinical setups of a voxelized model of a human head based on computer tomography data. Results are within 3% of the distal fall-off values obtained using Monte Carlo simulations.