Video compression is performed under multiple distortion constraints. Video coding includes determining a first set of Lagrangian cost values for multiple coding modes using a first distortion metric, determining a second set of Lagrangian cost values for the multiple coding modes using a second distortion metric, and selecting one of the coding modes based on the first set of Lagrangian cost values and the second set of Lagrangian cost values to encode a pixel block using the selected coding mode. The distortion metrics can include information associated with video display characteristics such as screen display size, video processing performance, a distortion characteristic, a temporal characteristic, or a spatial characteristic. The distortion metrics can also include characteristics of multiple video displays, such as parameters for usage, importance, design, and the technology type of the video displays.