We demonstrate a new technique to grow high-quality CdSe quantum films and islands with a very small sulfur contamination by using a cadmium sulfide compound source as Cd supply and additional Se flux. By monitoring the lattice constant with reflection high-energy electron diffraction, it is shown that the sulfur is almost completely substituted by Se and CdSe with a contamination below 5% sulfur is formed. The quantum structures obtained by the new method are generally of higher quality than those obtained by more conventional growth methods using elemental sources, even if migration enhanced methods were employed. With a brief growth interruption or post-growth annealing step the initially smooth CdSe layer can be reorganized into islands. The duration of this step as well as the initial amount of deposition allows a rather good control over the island formation. A strongly enhanced growth rate is observed for the first few monolayers of the ZnSe capping layer, which indicates a partial dissolution of the islands in the ZnSe growth front and Cd segregation.