For strained-layer epitaxy, a detailed examination is carried out of the way in which strain changes due to elemental segregation within the initially-formed flat “wetting” layer can control the Stranski—Krastanov epitaxial islanding transition. Based upon these considerations, it is shown that a new segregation-based mechanism is fully compatible with the transition in both the InxGa1−x As/GaAs and Si1−x Gex/Si systems grown over wide ranges of conditions. Quantitative segregation calculations allow critical “wetting” layer thicknesses to be derived and it is demonstrated that for the InxGa1−x As/GaAs system (x=0.25−1) such calculations show good agreement with experimental measurements. The strain energy associated with the segregated surface layer is determined for the complete range of deposited In concentrations using atomistic simulations. The segregation-mediated driving force is considered to be important, also, for all other epitaxial systems which comprise chemically-similar but substantially misfitting materials and which exhibit the Stranski—Krastanov transition.