Quantum-dot cellular automata (QCA), devices for computing through energy relaxation via quantum mechanical effects, promise high speed, very low power, and extremely high density. Steady progress has been made in implementing QCA; a small binary logic device has recently been manufactured and its logical switching behavior demonstrated. However, computation with hierarchical assemblies of primitive logic devices has not yet been demonstrated. Earlier work has shown that the four ground states of the originally proposed automata for implementing AND and OR are at slightly different energy levels. Because of this, certain combinations of these gates relax to ground states that encode an incorrect computation. A previously proposed construct, which essentially computes all four ground states simultaneously and thus evens out the disparities, works well under the idealized charge neutralization scheme originally proposed by the inventors of QCA. Unfortunately, under the more realistic image charge neutralization, the construction has only slightly better characteristics than the original gates and only then when the separation distance between the automaton and the metal layer generating the image charges is rather small.. This paper investigates methods for evening out the disparate ground states in the presence of image charge neutralization. Previously, it was shown that the more symmetric the automaton, the better its computational behavior under image charge neutralization. It is shown that adding symmetry also reduces the disparity in ground states and a new construct for balancing QCA logic gates is presented.