In an active matrix electroluminescent display device, an overall brightness level of an image to be displayed in a frame period is determined. A drive transistor of each pixel is controlled in dependence on an input drive signal for the pixel and on the overall brightness level, for example using a signal processor (30) to vary the pixel drive signals.This arrangement can control the pixels to limit the maximum currents drawn by the pixels, thereby limiting the cross talk effects resulting from voltage drops along row or column conductors. If an image is bright, the pixel drive levels across the image (or at least a part of the image) can be reduced, so that the maximum brightness is reduced.