Out-of-gamut problems exist in color image processing and color reproduction in different devices. Extensive research has been done on transforming out-of-gamut colors to the inside of the output device's color gamut for color reproduction. We focus on the out-of-gamut problem in color image processing. Luminance, hue, and saturation (LHS) and YIQ color coordinate systems are investigated. Efficient techniques for luminance and saturation processing and gamut clippings are presented. The efficient technique of luminance clipping for LHS is developed based on scaling, and the efficient technique of luminance clipping for YIQ is developed based on shifting. However, the efficient technique of saturation clipping for both LHS and YIQ is a combination of scaling and shifting. Such efficient techniques reduce the complexity of forward and backward transformations between the color representing the color coordinate system (RGB) and the processing color coordinate system (LHS or YIQ) significantly. Illustrations show the result of RGB, luminance, and saturation clippings. Saturation clipping is the best in terms of maintaining the hue and contrast of the original image. Experiments are also conducted to measure the efficiency of the proposed efficient techniques. It shows that the processing time is reduced by 27% comparing with the conventional technique using forward and backward color transformations.