Calibration targets are widely used to characterize imaging devices. The question addressed in this article is that of how many surfaces in a calibration target are needed to account for the performance of the whole target. Different to previous research where the problem of reducing calibration charts is addressed independently of the calibration problem; in this article we tackle the reduction question based on the calibration performance. We argue that the outcome of both spectral and colorimetric calibration is dependent on the properties of the cross-product matrix encompassing the color-signals. Further, we show that by careful mathematical manipulation it is possible to write the cross-product matrix as a linear sum of the submatrices corresponding to each individual color signal. This formulation allows us to cast the reduction problem as a quadratic minimization where we ask: given the spectral properties of the available color signals, what is the minimum number of surfaces needed to emulate the global cross-product matrix. To reduce the number of surfaces we impose an integer constraint on the minimization, where the weight of each surface can only assume a value of 1 or 0. Our results show that around 13 surfaces are sufficient to account of the 24 surfaces of the Macbeth color checker.