Display driver circuits are described for driving organic light emitting diode displays, particularly passive matrix displays, with greater efficiency. The display drivers comprise a controllable current generator to provide a variable current drive output to an OLED display, the current generator comprising at least one bipolar transistor in series with the current drive output. The display brightness is adjustable by controlling the current generator to vary the current drive to the display. Preferably the bipolar transistor has an emitter terminal substantially directly connected to a power supply line of the driver to reduce losses in the driver. A corresponding method is also described. By employing a bipolar transistor current drive and varying display brightness by controlling the current an efficient driver-display combination is obtained.