We show that polymer light-emitting diodes with high work-function cathodes and conjugated polyelectrolyte injection/transport layers exhibit excellent efficiencies despite large electron-injection barriers. Correlation of device response times with structure provides evidence that the electron-injection mechanism involves redistribution of the ions within the polyelectrolyte electron-transport layer and hole accumulation at the interface between the emissive and electron-transport layers. Both processes lead to screening of the internal electric field and a lowering of the electron-injection barrier. The hole and electron currents are therefore diffusion currents rather than drift currents. The response time and the device performance are influenced by the type of counterion used.