A display may have an array of pixels. Each pixel may have a light-emitting diode that emits light under control of a drive transistor. The organic light-emitting diodes may have a common cathode layer, a common electron layer, individual red, green, and blue emissive layers, a common hole layer, and individual anodes. The hole layer may have a hole injection layer stacked with a hole transport layer. Pixel circuits for controlling the diodes may be formed from a layer of thin-film transistor circuitry on a substrate. A planarization layer may cover the thin-film transistor layer. Lateral leakage current between adjacent diodes can be blocked by shorting the common hole layer to a metal line such as a bias electrode that is separate from the anodes. The metal line may be laterally interposed between adjacent pixels and may be formed on the planarization layer or embedded within the planarization layer.