DMSO-water mixtures exhibit a marked freezing point depression, reaching close to 60 K at n(DMSO) = 0.33. The phase diagram indicates that stable DMSO-water clusters may be responsible for this phenomenon, Using time-independent quantum chemical methods, we investigate possible candidates for stable supermolecules at mole fractions n(DMSO) = 0.25 and 0.33. The model clusters are built by adding various numbers of water molecules to a single DMSO molecule. Structures and interaction energetics are discussed in the light of experimental and theoretical results from the literature. A comparison with results from molecular dynamics simulations is of particular interest. Our optimized structures are spatially very different from those previously identified through MD simulations. To identify the structural patterns characterizing the clusters, we classify them on the basis of hydrogen-acceptor interactions. These are well separated on an interaction energy scale. For the hydrophobic interactions of the methyl groups with water, attractive interactions of up to 8 kJ/mol are found. In forming clusters corresponding to a range of different mole fractions, up to four water molecules are added to each DMSO molecule. This corresponds to a rough local model of solvation. Examination of the trends in the interactions indicates that the methyl-water interaction becomes more important upon solvation. Finally, we investigate how the clusters interact and attempt to explain which role is played by the various structures and their intercluster interaction modes in the freezing behavior of DMSO-water.