Propose a methodology for fast best-match retrieval of structured images. A triangle inequality property for the tree-distance introduced by Oflazer (1997) is proven. This property is, in turn, applied to obtain a saturation algorithm of the trie used to store the database of the collection of pictures. The new approach can be considered as a substantial optimization of Oflazer's technique and can be applied to the retrieval of homogeneous hierarchically structured objects of any kind. The new technique inscribes itself in the number of distance-based search strategies and it is of interest for the indexing and maintenance of large collections of historical and pictorial data. We demonstrate the proposed approach on an example and report data about the speed-up that it introduces in query processing. Direct comparison with an MVP-trees algorithm is also presented.