Existing digital image composition algorithms neglect the out-of-gamut problem, i.e. some pixel values in a composited image exceed the displayable or printable range. In this paper, we show that the commonly used solution, i.e. hard clipping or linear scaling, results in either detail loss or global contrast reduction. Directly applying the existing high dynamic range (HDR) compression algorithms cannot achieve pleasant visual quality either. Thus, we propose a gamut fitting method to solve this out-of-gamut problem in image composition. In particular, we formulate gamut fitting as a multi-criteria optimization problem. Polynomials in the Bernstein-Bézier form are used to compute the optimal gamut mapping curve. The proposed approach can be regarded as a post-processing procedure to enhance the visual quality of the resulting images from image composition applications.