A display may have an array of display pixels. Digital display data may be received by a digital-to-analog converter that converts the digital display data to analog display data. The magnitudes of the analog display data signals can be controlled by a regulated voltage received by the digital-to-analog converter. A brightness controller may have multiple peak luminance control (PLC) profiles. In accordance with an embodiment, a brightness setting may be processed by a lookup table to identify a pair of PLC profiles that is interpolated in order to obtain the desired regulated voltage. In accordance with another embodiment, a single PLC profile may be used that is a function of a combined parameter that takes into account both average frame luminance and the brightness setting. In accordance with yet another embodiment, a lookup table that specifies brightness setting offset values may be used to directly modulate the brightness setting.