1. A method of controlling backlighting of a plurality of portions (“blocks”) of a block-controllable display, the blocks being arranged in a two-dimensional array that is co-extensive with the display, a block including multiple pixels of the display, and a block having a respective backlight whose viewer-perceived brightness is controllable independently of the viewer-perceived brightness of other of the backlights, the method comprising for successive frames of image information supplied for display by the display: determining a composite grayscale value for a block from the image information for that block; identifying a block as either still or moving depending on whether the image information for that block is still or moving, respectively; additionally identifying a block that is immediately adjacent to a moving block as a filtered block; for a block that is identified only as still, determining a backlight brightness value by applying a first brightness function to the composite grayscale value for that block; for a block that is identified only as moving, determining a backlight brightness value by applying a second brightness function to the composite grayscale value for that block; for a block that is identified as both filtered and still, determining a backlight brightness value as the greater of (a) a first intermediate backlight brightness value from applying the first brightness function to the composite grayscale value for that block, and (b) a second intermediate backlight brightness value from applying a third brightness function to the greatest composite grayscale value of any moving block that is adjacent to that block; for a block that is identified as both filtered and moving, determining a backlight brightness value as the greater of (a) a third intermediate backlight brightness value from applying the second brightness function to the composite grayscale value for that block, and (b) the second intermediate backlight brightness value for that block; and using the backlight brightness value determined for a block in control of the brightness of the backlight of that block.