In an optical trap, micron-sized dielectric particles in aqueous solutions can be held by a tightly focused laser beam. The optical force on the particle is composed of an attractive gradient force and a destabilizing scattering force. To optimize the trapping potential, we reduced the scattering force by using coated microspheres. The shell of the particle was designed such that it acts as an anti-reflection coating. We made and characterized such particles and found that in comparison with the uniform microspheres of the same diameter a more than two-fold stiffening of the trap. Compared to larger spheres, we achieved an increase in trap stiffness of up to 10-fold. These results quantitatively agree with our calculations based on the generalized Lorenz-Mie theory. By improving the trapping potential higher overall forces can be achieved with the same laser power, or vice versa the same force can be reached by using less laser power. A higher maximal force increases the range of possible experiments, and a reduced laser intensity leads to less photo-toxic interactions or laser heating relevant for biological applications.