Contrary to simple expectations about increasing hydrophobicity, successive methylation of ammonia (NH3) does not yield a monotonic increase in the observed solvation free energies; in fact, NH2CH3 is found to be more soluble than NH3. Previous free energy calculations have not reproduced the trend in experimental values. Here, we perform the perturbations NH3 --> NH2CH3 and NH3 --> N(CH3)(3) with explicitly polarizable water and solute. Although the increases in solvation energy with methyl substitution are smaller than with a pairwise-additive model, the methylamines are still calculated to be hydrophobic compared to ammonia. The computed relative solvation energies and solute dipole moments, however, agree remarkably well with previous results obtained with a different implementation of polarizability.