Demonstrations of high-quality electron beams driven by compact and 10 Hz repetition rate lasers have been recently achieved by several research teams. We report in this paper numerical study results of an optimized conversion of these energetic electrons into high-energy photons, through the bremsstrahlung process in a dense material. Dedicated optimizations of the spectral and optical qualities of such resulting photon beams are carried out by Monte Carlo simulations and by considering typical measurements of electron beams obtained with a 30 TW–30 fs laser. These results of simulations show the possibility of production of gamma-ray sources with optimal and tunable dose, temperature, size and angular divergence. Gamma sources with size below 50 μm are expected to be produced using such compact laser-plasma accelerators.