Three-way decomposition is applied for the structural analysis of a complete three-dimensional (15)N-NOESY-HSQC of the 128 residues long protein azurin. The procedure presented includes decomposition using the software MUNIN, providing an initial characterization of the complete spectrum by 355 components. This is followed by post-processing yielding a final list of 149 components, 123 of which characterize 1859 NOE peaks from backbone N-H groups. Components from three-way decomposition are defined as direct products of one-dimensional shapes along the three dimensions. Thus, a complete set of distance constraints from this spectrum is obtained by one-dimensional peak picking of the shapes along the NOE dimension. Correctness and completeness of this set of NOEs are tested for all backbone amide groups against both an independent peak picking algorithm and the three-dimensional crystal structure of azurin, and a coincidence of about 95% is observed. Automated 'demixing' of components that are 'mixed' in a complex manner due to overlap of the HN and/or (15)N frequencies is illustrated.