We report a photometric study of ultra-efficient light emitting diodes (LEDs) that exhibit superior color rendering index (CRI) and luminous efficacy of optical radiation (LER) using semiconductor quantum dot nanocrystal (NC) luminophores. Over 200 million systematically varied NC-LED designs have been simulated to understand feasible performance in terms of CRI vs. LER. We evaluated the effects of design parameters including peak emission wavelength, full-width-at-half-maximum, and relative amplitudes of each NC color component on LED performance. Warm-white LEDs with CRI >90 and LER >380 lm/W at a correlated color temperature of 3000 K are shown to be achieved using nanocrystal luminophores.