An electronic device such as a wristwatch device or other device may have a display. The display may be used to continuously display information such as watch face information. A watch face image on the display may contain watch face elements such as watch face hands, watch face indices, and complications. To reduce burn-in risk for watch face elements, control circuitry in the electronic device may impose burn-in constraints on attributes of the watch face elements such as peak luminance constraints, dwell time constraints, color constraints, constraints on the shape of each element, and constraints on element style. These constraints may help avoid situations in which static elements such as watch face indices create more burn-in than dynamic elements such as watch face hands.