We show that the islands formed in Stranski-Krastanow (SK) growth of Ge on Si(100) are initially dislocation free. Island formation in true SK growth should be driven by strain relaxation in large, dislocated islands. Coherent SK growth is explained in terms of elastic deformation around the islands, which partially accommodates mismatch. The limiting critical thickness, hc, of coherent SK islands is shown to be higher than that for 2D growth. We demonstrate growth of dislocation-free Ge islands on Si to a thickness of ~=500 Å, 50×higher than hc for 2D Ge/Si epitaxy.