A display may have an array of organic light-emitting diode display pixels. Each display pixel may include a drive transistor coupled in series with one or more emission transistors and a respective organic light-emitting diode (OLED). A semiconducting-oxide transistor may be coupled between a drain terminal and a gate terminal of the drive transistor to help reduce leakage during low-refresh-rate display operations. To compensate for variations in the threshold voltage of the semiconducting-oxide transistor, the magnitude of a high voltage level of a scan control signal provided to the gate terminal of the semiconducting-oxide transistor may be adjusted. Sensing circuitry may be used to sense a display current while displaying a calibration image. The sensed display current may be compared to an expected display current associated with the calibration image. Processing circuitry may update the high voltage level based on the actual display current compared to the expected display current.