Compact tuneable sources of ultrashort hard x-ray pulses can be realized by Thomson scattering, taking advantage
of the comparatively short wavelength of a scattered laser pulse with respect to the period length of
conventional undulators. Here, we present a detailed analysis and optimization of the efficiency of linear and
non-linear Thomson scattering when the process is driven with relativistic laser pulses and when the conventional
accelerator is replaced by a laser-plasma wakefield accelerator.