In this paper, we present new optimization techniques for the recently introduced Majority-Inverter Graph (MIG). Our optimizations exploit intrinsic algebraic properties of MIGs and aim at rewriting the complemented edges of the graph without changing its shape. Two exact algorithms are proposed to minimize the number of complemented edges in the graph. The former is a dynamic programming method for trees; the latter finds the exact solution with a minimum number of inversions using Boolean satisfiability (SAT). We also describe a heuristic rule based algorithm to minimize complemented edges using local transformations. Experimental results for the exact algorithm to fanout-free regions show an average reduction of 12.8% on the EPFL benchmark suite. Applying the heuristic method on the same instances leads to a total improvement of 60.2%.