Algebraic multigrid (AMG) is an effective iterative solver for systems of linear equations. The Galerkin product, an essential component to the setup phase of AMG, causes fill-in on the coarse grids. In parallel implementations of AMG, this added density to coarse levels yields an increase in communications costs, reducing the scalability of the method. As problem size grows, the number of levels in the hierarchy will increase, yielding increasingly large, dense levels. The communication costs can be reduced through the use of non-Galerkin coarse grids, in which unnecessary entries are removed reintroducing sparsity to the coarser levels. A study of the parallel performance of GMRES preconditioned by non-Galerkin shows a consistent decrease in solve times for a three dimensional Laplace problem. The setup times show that any added cost to this phase is masked by the reduction in communication, and the overall time spent in the setup phase is often also reduced. Further tests show increasing the tolerance for collapsing entries on coarser grids has added benefits of removing the larger percentage of unnecessary entries occurring further in the hierarchy. Retaining symmetry of coarse grids allows use of more competitive methods such as CG or its three-term analogue for indefinite matrices, minimal residual method.