The size distribution and chemical composition of aerosol particles during a dust storm in the eastern Mediterranean are analyzed. The data were obtained from airborne measurements during the Mediterranean Israeli Dust Experiment (MEIDEX). The dust storm passed over the Mediterranean Sea and extended up to an altitude of about 2.5 km. The uniqueness of this dust storm is that approximately 35% of the coarse particles up to about 1 km in height were internally mixtures of mineral dust and sea salt. Just north of the dust storm, large convective clouds developed, and heavy rain was recorded by the radar on the Tropical Rainfall Measuring Mission satellite. The chemical and physical properties of the particles are used as initial conditions for conducting a sensitivity simulation study with the two-dimensional detailed spectral bin microphysical model of Tel Aviv University. The simulations show that ignoring the ice-nucleating ability of the mineral dust, but allowing the soluble component of the mixed aerosols to act as efficient giant cloud condensation nuclei (CCN), enhances the development of the warm rain process in continental clouds. In our simulations the rain amounts increased by as much as 37% compared to the case without giant CCN. Introducing similar coarse-mode particles into more maritime-type clouds does not have significant effect on the cloud or on the amount of rainfall. On the other hand, allowing the mineral dust particles to also act as efficient ice nuclei (IN) reduces the amount of rain on the ground compared to the case when they are inactive. The simulations also reveal that under the same profiles of meteorological parameters, maritime clouds develop precipitation earlier and reach lower altitudes than continental clouds. When the dust particles are active as both giant CCN and effective IN, the continental clouds become wider, while the effects on the more maritime clouds is very small.