We report on the efficacy of a novel design for dielectric laser accelerators by adding a distributed Bragg reflector (DBR) to a dual pillar grating accelerating structure. This mimics a double-sided laser illumination, resulting in an enhanced longitudinal electric field while reducing the deflecting transverse effects when compared to single-sided illumination. We improve the coupling efficiency of the incident electric field into the accelerating mode by 57%. The 12 μm long structures accelerate sub-relativistic 28 keV electrons with gradients of up to 200 MeV/m in theory and 133 MeV/m in practice. This Letter shows how lithographically produced nano-structures help to make novel laser accelerators more efficient.