Detection of a target object in a radiological image is often impeded by an obscuring background "clutter" resulting from the contrast between various materials in the neighborhood of the target. Dual-energy techniques can reduce or remove this clutter. In order for the target to be detectable in the image after dual-energy processing, the signal-to-noise ratio (SNR), defined as the difference between the target and the background divided by the photon noise in the difference, must exceed some threshold. A given SNR may be obtained for a wide range of the energies of the two x-ray beams and the ratio of their fluences. A theoretical model is developed which permits the choice of beams to be optimized with respect to some critical parameter--in this case, patient dose. The analysis is applied to the detection of calcifications in mammography. For an ideal imaging system, we predict that the optimum beam energies are 19 and 68 keV. A dose of 0.42 cGy is required to obtain an SNR of 5 for detection of a 0.02-cm cubic calcification in the resulting clutter-free image. This can be reduced to 0.16 cGy if the higher energy image is smoothed, prior to dual-energy processing, such that its variance is reduced to one-fourth of its unsmoothed value.