In a recent paper (Kvamme (1995)) I suggested a dielectrically adjusted version of the RISM equation for the situation of ions in mixed solvents. In the present work I apply this theory to model mixtures of water with methanol or with ethanol. Calculated structures from the integral equation theory are compared with the corresponding results from NVT molecular dynamics simulations. The results for water + ethanol indicate that the integral equation results are rather sensitive to the short range hydrogen core on methanol. For several of the partial correlation functions the agreement between integral equation theory and molecular dynamics simulations is good. However, unlike the results from molecular simulations, the results from integral equation theory appear to be sensitive to the short range core of the charged hydrogen atoms. A similar type of behaviour is observed in the model system of water and ethanol. Because of this difference in sensitivity of the short range of the charged hydrogens, it is not possible at this stage to draw rigorous conclusions as to the quality of the predictions from the integral equation theory.