Recently we proposed a novel method of alignment-alignment comparison, COMPASS (the tool for COmparison of Multiple Protein Alignments with Assessment of Statistical Significance). Here we present several examples of the relations between PFAM protein families that were detected by COMPASS and that lead to the predictions of presently unresolved protein structures. We discuss relatively straightforward COMPASS predictions that are new and interesting to us, and that would require a substantial time and effort to justify even for a skilled PSI-BLAST user. All of the presented COMPASS hits are independently confirmed by other methods, including the ab initio structure-prediction method ROSETTA. The tertiary structure predictions made by ROSETTA proved to be useful for improving sequence-derived alignments, because they are based on a reasonable folding of the polypeptide chain rather than on the information from sequence databases. The ability of COMPASS to predict new relations within the PFAM database indicates the high sensitivity of COMPASS searches and substantiates its potential value for the discovery of previously unknown similarities between protein families.