The development of white organic light-emitting diodes (OLEDs) holds great promise for the production of highly efficient large-area light sources. High internal quantum efficiencies for the conversion of electrical energy to light have been realized. Nevertheless, the overall device power efficiencies are still considerably below the 60-70 lumens per watt of fluorescent tubes, which is the current benchmark for novel light sources. Although some reports about highly power-efficient white OLEDs exist, details about structure and the measurement conditions of these structures have not been fully disclosed: the highest power efficiency reported in the scientific literature is 44 lm W(-1) (ref. 7). Here we report an improved OLED structure which reaches fluorescent tube efficiency. By combining a carefully chosen emitter layer with high-refractive-index substrates, and using a periodic outcoupling structure, we achieve a device power efficiency of 90 lm W(-1) at 1,000 candelas per square metre. This efficiency has the potential to be raised to 124 lm W(-1) if the light outcoupling can be further improved. Besides approaching internal quantum efficiency values of one, we have also focused on reducing energetic and ohmic losses that occur during electron-photon conversion. We anticipate that our results will be a starting point for further research, leading to white OLEDs having efficiencies beyond 100 lm W(-1). This could make white-light OLEDs, with their soft area light and high colour-rendering qualities, the light sources of choice for the future.