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The energy-overlap problem in Laue diffraction often makes a Laue diffraction data set incomplete in a systematic way: low-resolution reflections more commonly overlap with other reflections than do reflections at higher resolution. We describe the development and testing of a harmonic deconvolution procedure that resolves energy overlaps accurately and is based on the wavelength-normalization curve obtained from single reflections. The conditions for satisfactory harmonic deconvolution are identified by examination of a series of data sets that differ in their redundancy. This procedure has been incorporated in the software system LaueView [Ren & Moffat (1995). J. Appl. Cryst. 28, 461–481]. Results on Laue data sets from crystals of lysozyme and α-haemolysin demonstrate that Laue data sets can be more than 90% complete even at 10 Å resolution and that structure amplitudes derived from these deconvoluted multiples can be as accurate as those derived from the best monochromatic data.