► The Richardson–Lucy-Algorithm was applied to very high-energy gamma-ray images. ► Systematic studies of the RLA with respect to source characteristics were performed. ► Deconvolution allows to study structural details below instrumental angular resolution. ► Deconvolution is applicable on 2 of the known 5 VHE shell-type SNRs. The Richardson–Lucy deconvolution algorithm was applied to astronomical images in the very high-energy regime with photon energies above 100GeV. Through a systematic study with respect to source significance, background level and source morphology we were able to derive optimal deconvolution parameters. The results presented show that deconvolution makes it possible to study structural details well below the angular resolution of the very high-energy γ-ray experiment.