A problem common to computer programs for structure elucidation is the efficient and prospective use of the input information to constrain the structure generation process. The input may consist of potentially overlapping substructure requirements and alternative substructure interpretations of spectral data. Other useful information may be structural features that must not be present in the output structures. All of these may interact in a complex manner that is impossible to determine by use of a bond-by-bond structure assembly algorithm. A new method is described called structure reduction. In contrast to structure assembly, this method begins with a set of all bonds and removes inconsistent bonds as structure generation progresses. This results in a more efficient use of the input information and the ability to use potentially overlapping required substructures. Several examples illustrate the application of our computer program COCOA, which uses this method to solve real-world structure elucidation problems.