Baryonic number conservation and 't Hooft anomaly equations select only a few candidate models for composite quarks and leptons. We carry out a systematic group-theoretical search and find that composite-component duality is the characteristic feature allowing for baryon conservation. Complementarity between the symmetric and the broken phases naturally fits within dual composite models and allows for the solution of the anomaly equations. The study suggests subcolor groups SU(9) or SU(7) with two color singlets and two color antitriplets of subcomponents, or with two singlets, one triplet and one antitriplet, or analogous situations with O(17) and O(15). Finally we discuss a dual-complementary pattern of different layers of compositeness using elementary Higgs at intermediate stages.