Achieving balanced electron-hole injection and perfect recombination of the charge carriers is central to the design of efficient polymer light-emitting diodes (LEDs). A number of approaches have focused on modification of the injection contacts, for example by incorporating an additional conducting-polymer layer at the indium-tin oxide (ITO) anode. Recently, the layer-by-layer polyelectrolyte deposition route has been developed for the fabrication of ultrathin polymer layers. Using this route, we previously incorporated ultrathin (<100 A) charge-injection interfacial layers in polymer LEDs. Here we show how molecular-scale engineering of these interlayers to form stepped and graded electronic profiles can lead to remarkably efficient single-layer polymer LEDs. These devices exhibit nearly balanced injection, near-perfect recombination, and greatly reduced pre-turn-on leakage currents. A green-emitting LED comprising a poly(p-phenylene vinylene) derivative sandwiched between a calcium cathode and the modified ITO anode yields an external forward efficiency of 6.0 per cent (estimated internal efficiency, 15-20 per cent) at a luminance of 1,600 candelas per m2 at 5 V.