The amalgamation of two incomplete self-sorting processes into a process that makes quantitative use of all members of the library is described by 2-fold completive self-sorting. Toward this goal, individual metal-ligand binding scenarios were optimized for high thermodynamic stability and best selectivity, by screening a variety of factors, such as steric and electronic effects, pi-pi interactions, and metal-ion specifics. Using optimized, heteroleptic metal-ligand binding motifs, a library of four different ligands (1, 2, 3, 4) and two different metal ions (Zn2+, Cu+) was set up to assess 2-fold completive self-sorting. Out of 20 different combinations, the self-sorting library ended up with only two metal-ligand complexes in basically quantitative yield. To demonstrate the value of 2-fold completive self-sorting for the formation of nanostructures, the optimized, highly selective binding motifs were implemented into three polyfunctional ligands. Their integrative self-sorting in the presence of Zn2+ and Cu+ led to the clean formation of the supramolecular trapezoid T, a simple but still unknown supramolecular architecture. The dynamic trapezoid T consists of three different ligands with four different donor-acceptor interactions. Its structure was established by H-1 NMR spectroscopy, electrospray ionization mass spectroscopy, and differential pulse voltammetry (DPV) and by exclusion of alternative structures.