1. Ink jet image producing device for the reproduction of digital image data of photographic images, comprising at least one printing head selected from the group of a printing head and a printing head arrangement, with more than three colors selected from the group of base colors and ink jet colors, which colors stretch a color space; a computing device for calculating at least one of the location and color coordinates of color values of image data in the color space; a determining device for determining with which colors or color mixtures, and at which color densities, altogether referred to as—color set—, the color data of the image data can be reproduced; a threshold device including at least one threshold for a degree of coverage of at least one printing medium; an evaluation device for evaluating whether a determined color set requires a larger or smaller ink amount the threshold device being constructed for selecting one of the color sets depending on the threshold for the printing medium used; and a print head control device for printing the image data by way of a printing head and with the selected color set: