Strain engineering and the crystalline quality of semiconductor nanostructures are important issues for electronic and optoelectronic devices. We report on defect-free SiGe island arrays resulting from Ge coverages of up to 38 monolayers grown on prepatterned Si(001) substrates. This represents a significant expansion of the parameter space known for the growth of perfect island arrays. A cyclic development of the Ge content and island shape was observed while increasing the Ge coverage. Synchrotron-based x-ray diffraction experiments and finite element method calculations allow us to study the strain behavior of such islands in great detail. In contrast to the oscillatory changes of island shape and average Ge content, the overall strain behavior of these islands exhibits a clear monotonic trend of progressive strain relaxation with increasing Ge coverage.