Long-period (LP) seismicity on volcanoes is thought to be associated with moving fluids or resonating fluid-filled conduits, hence LP moment tensor (MT) source inversions might have a direct bearing on our understanding of the plumbing system. Using 3-D full wavefield simulations and 2-D sensitivity kernels in a digital elevation model of Mount Etna, we investigate the influence of near-surface volcanic structure on LP signals and on moment tensor inversions. Contrary to common wisdom in crustal seismology we find that, despite their relatively long wavelengths, LPs are severely distorted by near-surface structures including layering and topographic features. In particular near-surface low-velocity structures which are commonly observed on volcanoes play a critical role in controlling the nature of LP signals. If not accounted for, these path effects leak into the source solution, leading to the emergence of erroneous source geometries, spurious forces and incorrect source time functions. This is particularly problematic if one adopts an “unconstrained” solution space for the source, with many free parameters. Hence there is a fine balance in the trade-off between the velocity model and the source. In the absence of high-resolution near-surface velocity control we demonstrate the importance of employing a priori source information from other fields (e.g., structural geology), for shallow LPs, constraining the number of free parameters in the inversion. A probabilistic approach should then be taken, as the model with the “best fit” is not necessarily the “true” solution.