Strain engineering during the capping of III-V quantum dots has been explored as a means to control the height of strained self-assembled quantum dots. Results of Kinetic Monte Carlo simulations are confronted with cross-sectional Scanning Tunnel Microscopy (STM) measurements performed on InAs quantum dots grown by molecular beam epitaxy. We studied InAs quantum dots that are capped by InxGa(1x)As layers of different indium compositions. Both from our realistic 3D kinetic Monte Carlo simulations and the X-STM measurements on real samples, a trend in the height of the capped quantum dot is found as a function of the lattice mismatch between the quantum dot material and the capping layer. Results obtained on additional material combinations show a generic role of the elastic energy in the control of the quantum dot morphology by strain engineering during capping.