We report a detailed study of InAs/GaAs quantum dot (QD) structures grown by molecular beam epitaxy with InAs coverages θ continuously graded from 1.5 to 2.9 ML. The effect of coverage on the properties of QD structures was investigated by combining atomic force microscopy, transmission electron microscopy, x-ray diffraction, photoluminescence, capacitance-voltage, and deep level transient spectroscopy. In the 1.5–2.9 ML range small-sized coherent QDs are formed with diameters and densities that increase up to 15 nm and 2×1011 cm−2, respectively. For θ>2.4 ML large-sized QDs with diameters of 25 nm and densities ranging from 2×108 to 1.5×109 cm−2 coexist with small-sized QDs. We explain the occurrence of large-sized QDs as the inevitable consequence of ripening, as predicted for highly lattice-mismatched systems under thermodynamic equilibrium conditions, when the coverage of the epitaxial layer exceeds a critical value. The fraction of ripened islands which plastically relax increases with θ, leading to the formation of V-shaped defects at the interface between QDs and upper confining layers that propagate toward the surface. Island relaxation substantially affects the properties of QD structures: (i) free carrier concentration is reduced near the QD plane, (ii) the QD photoluminescence intensity is significantly quenched, and (iii) deep levels show up with typical features related to extended structural defects.