Highly efficient organic light-emitting diodes (OLEDs) are strongly demanded for both display and illumination applications. High efficiency would also help prolong the device lifespan. However, many OLEDs encounter significant roll-off problems, leading to undesired low device efficiency at high luminance, which is unfavorable to their commercial realization for lighting. Hence, OLED devices with mild or even little roll-off are highly expected. We have, nevertheless, observed some OLEDs that exhibit roll-up phenomenon, i.e., that their external quantum efficiency (EQE) or current efficiency increases as the applied voltage or brightness is increased. By taking such advantage of device architecture design, OLEDs with an approaching or even above the theoretical limit EQE are obtained at high luminance. In this report, we present how this works for a yellow OLED that exhibits a record-high power efficiency among reported fluorescent yellow OLEDs, a very-low color temperature OLED with a record-breaking efficacy based on the same color-temperature, and a green OLED. Notably, the yellow OLED exhibits an EQE that increases from 5.4 to 6.2% and current efficiency from 16.4 to as the luminance increases from 1000 to . Plausible mechanisms regarding why roll-up occurs in these devices are discussed.