Growth of multi-layered arrays of quantum dots (QDs) allows efficient wave function engineering. New approaches to the control of geometrical and electronic parameters of QD structures are developed. The variation of spacer thickness results in transitions between vertically correlated and vertically anticorrelated growth of islands in successive sheets. The growth of very small QDs in the first sheet governs the density and the size of QDs of the successive sheets. The overgrowth of QDs by an alloy material results in an activated phase separation in the cap layer and may lead to substantial increase in the effective size of the QDs and to a redshift of the electronic spectrum.