In an optical trap, micron-sized dielectric particles are 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. We hypothesized that using anti-reflection-coated microspheres would reduce scattering and lead to stronger trapping. We found that homogeneous silica and polystyrene microspheres had a sharp maximum trap stiffness at a diameter of around 800 nm--the trapping laser wavelength in water--and that a silica coating on a polystyrene microsphere was a substantial improvement for larger diameters. In addition, we noticed that homogeneous spheres of a correct size demonstrated anti-reflective properties. Our results quantitatively agreed with Mie scattering calculations and serve as a proof of principle. We used a DNA stretching experiment to confirm the large linear range in detection and force of the coated microspheres and performed a high-force motor protein assay. These measurements show that the surfaces of the coated microspheres are compatible with biophysical assays.