Tagged photons from 81 to 116 MeV were used to measure elastic Compton scat- tering cross sections from deuterium and carbon targets at the MAX-lab facility in Lund. Scattered gamma rays were detected in three very large NaI(Tl) crystals with sufficient energy resolution to isolate deuterium elastic yields at scattering angles of 60°, 90°, 120° and 150°. Calculations indicate that back-angle Compton scattering on deuterium in this energy range is sensitive to the electric and magnetic polarizabilities of the nucleon. Results of this research were obtained with improved beam tagging system conditions compared to previous elastic Compton scattering experiments from deuterium.