An electronic device may be provided with a phased antenna array having a dielectric resonator antenna. The antenna may include a first dielectric block on a printed circuit, a second dielectric block on the first dielectric block, and a third dielectric block on the second dielectric block. At least the second and third dielectric blocks may have different dielectric constants. A parasitic element may be disposed between the second and third dielectric resonating elements and/or a parasitic element may be disposed on a radiative face of the third dielectric resonating element. The parasitic elements may act as electromagnetic mirrors that form images of electric fields in the dielectric resonating elements. The images may make the dielectric resonating elements exhibit a greater electromagnetic height than physical height. This may allow for a reduction in the overall physical height of the dielectric resonator antenna without sacrificing wireless performance.