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Presently two new research facilities are either already under construction ('MEGa-Ray' at Lawrence Livermore National Laboratory/US) or soon ready to start construction (ELI-Nuclear Physics in Bucharest/ Romania), both aiming to provide highly brilliant γ beams with so far unprecedented properties (ca. 1013 photons/s, energy resolution ≤10-13 via Compton-backscattering of laser photons from a high-quality relativistic electron beam. With these intense, monochromatic γ beams, a new era of photonuclear physics will be enabled. It is envisaged to exploit the novel beams for highly-selective studies of extremely deformed nuclei in the multiple-humped potential energy landscape of the actinides via photofission. We will be able to populate gateway states in the first potential minimum of nuclei, predominantly originating from collective states in the (superdeformed) second or (hyperdeformed) third potential minimum, tunnelling back into the first well. The γ beam energy resolution of 10-13 allow to resolve individual resonances due to the lower level density in the higher potential minima. Excited states in these minima can be rather selectively populated with much larger intensities than achieved with former methods based on light-ion induced reactions. Also the large background from prompt fission with σisomer/σprompt ≈10-5 is avoided. Hence a detailed γ spectroscopy in the second and third minimum will be enabled. [ABSTRACT FROM AUTHOR]