Ex situ observed growth stages of LPE-iGe/Si(001) Stranski-Krastanow islands with a germanium content of 10% give clear evidence of a rapid shape transition at one third of the final island height. The island shape changes from a lenslike type without a top facet to truncated pyramids with {111} side facets and an (001) top facet. High-resolution x-ray diffraction has been applied to islands with higher germanium content of about 30%. Experimental results are compared with respective kinematical scattering simulations based on finite element calculations for the strain field. From these simulations the three-dimensional germanium composition profile inside the islands can be extracted and it substantiates a similar growth scenario with a distinct shape transition at one third of the final island height also for this germanium concentration range. We attribute the observed finite island size to a distinct nucleation problem at the island bottom caused by exceptional high strain energy around the island corners in combination with a strain driven wetting layer depression.