A <i>Majority-Inverter Graph</i> (MIG) is a recently introduced logic representation form whose algebraic and Boolean properties allow for efficient logic optimization. In particular, when considering logic depth reduction, MIG algorithms obtained significantly superior synthesis results as compared to the state-of-the-art approaches based on AND-inverter graphs and commercial tools. In this paper, we present a new MIG optimization algorithm targeting size minimization based on functional hashing. The proposed algorithm makes use of minimum MIG representations which are precomputed for functions up to 4 variables using an approach based on <i>Satisfiability Modulo Theories</i> (SMT). Experimental results show that heavily-optimized MIGs can be further minimized also in size, thanks to our proposed methodology. When using the optimized MIGs as starting point for technology mapping, we were able to improve both depth and area for the arithmetic instances of the EPFL benchmarks beyond the current results achievable by state-of- the-art logic synthesis algorithms.