The technological development in the field of high brightness linear accelerators and high energy/high quality lasers enables today designing high brilliance Compton-X and Gamma-photon beams suitable for a wide range of applications in the innovative field of nuclear photonics. The challenging requirements of this kind of source comprise: tunable energy (1-20 MeV), very narrow bandwidth (0.3%), and high spectral density (10 4 photons/s/eV). We present here a study focused on the design and the optimization of an electron Linac aimed to meet the source specifications of the European Extreme Light Infrastructure-Nuclear Physics project, currently funded and seeking for an innovative machine design in order to outperform state-of-the-art facilities. We show that the phase space density of the electron beam, at the collision point against the laser pulse, is the main quality factor characterizing the Linac. V C 2013 AIP Publishing LLC. [http://dx