We study the effective action of quantum mechanical SU(N) Yang-Mills theories with sixteen supersymmetries and N > 2. We show that supersymmetry requires that the eight fermion terms in the supersymmetric completion of the v⁴ terms be one-loop exact. We also show that the twelve fermion terms in the supersymmetric completion of the v⁶ terms are two-loop exact for N = 3. For N > 3, this no longer seems to be true; we are able to find non-renormalization theorems for only certain twelve fermion structures. We call these structures `generalized F-terms.' We argue that as the rank of the gauge group is increased, there can be more generalized F-terms at higher orders in the derivative expansion.