Knowledge about Setschenow salting constants, KS, the exponential dependence of Henry's Law coefficients on salt concentration, is of particular importance to predict secondary organic aerosol (SOA) formation from soluble species in atmospheric waters with high salt concentrations, such as aerosols. We have measured KS of glyoxal and methylglyoxal for the atmospherically relevant salts (NH4)2SO4, NH4NO3, NaNO3, and NaCl and find that glyoxal consistently "salts-in" (KS of -0.16, -0.06, -0.065, -0.1 molality(-1), respectively) while methylglyoxal "salts-out" (KS of +0.16, +0.075, +0.02, +0.06 molality(-1)). We show that KS values for different salts are additive and present an equation for use in atmospheric models. Additionally, we have performed a series of quantum chemical calculations to determine the interactions between glyoxal/methylglyoxal monohydrate with Cl(-), NO3(-), SO4(2-), Na(+), and NH4(+) and find Gibbs free energies of water displacement of -10.9, -22.0, -22.9, 2.09, and 1.2 kJ/mol for glyoxal monohydrate and -3.1, -10.3, -7.91, 6.11, and 1.6 kJ/mol for methylglyoxal monohydrate with uncertainties of 8 kJ/mol. The quantum chemical calculations support that SO4(2-), NO3(-), and Cl(-) modify partitioning, while cations do not. Other factors such as ion charge or partitioning volume effects likely need to be considered to fully explain salting effects.