Absolute photonic band gaps in two-dimensional square and honeycomb lattices of circular cross-section rods can be increased by reducing the structure symmetry. The addition of a smaller diameter rod into the center of each lattice unit cell lifts band degeneracies to create significantly larger band gaps. Symmetry breaking is most effective at filling fractions near those which produce absolute band gaps for the original lattice. Rod diameter ratios in the range 0.1–0.2 yield the greatest improvement in absolute gap size. Crystal symmetry reduction opens up new ways for engineering photonic gaps.