Conventionally, the main design parameters for the color gamut of a display are the area in chromaticity space and peak white. This suits normal-gamut 3-primary display design, but is not sufficient for designing wide gamut displays, especially if the display has more than three primaries. In this paper, we propose using the optimal color stimuli as a target for gamut design and illustrate this for displays with 3 to 6 primaries. Applying the design target to a display with an additional white primary (RGBW) [1] confirms that such a display may both have a wide gamut and high peak brightness, but also shows that saturated colors are more difficult to render. Furthermore, the analysis shows that an RGB display is attractive for color rendering and that a display with double red, green, blue, yellow and cyan primaries (see e.g. [2]) can provide a good balance between efficiency and gamut.