The self-assembly reactions of tetratopic metal acceptors with the flexible bidentate ligands are known to yield self-assembled molecular squares of the type [M4L8], triangles of composition [M3L6], or a mixture of these two. In this work, we demonstrate the preferential formation of a trimeric cage assembly of the formula [Pd3(L1)6·(BF4)6] (1a) over the tetrameric cage [Pd4(L1)8·(BF4)8] (1b) by employing a flexible dipodal phosphoramide ligand, [PhPO(NH(3-Py))2] (L1; 3-Py = 3-aminopyridine), in a reaction with [Pd(CH3CN)4·(BF4)2]. The entropically favored trimeric self-assembly of 1a is the predominant species in the solution [dimethyl sulfoxide (DMSO)-d6] at room temperature. In fact, at higher temperatures, 1a was found to be the only product, as observed from the disappearance of the peak due to 1b in the 31P NMR spectrum. However, in a 1:1 mixture of acetonitrile (MeCN)-d3 and DMSO-d6, the tetrameric species 1b is the preferred species, as revealed by the 31P NMR and electrospray ionization mass spectral analyses. The structure of the molecular trimer 1a has been established in the solid state by using single-crystal X-ray diffraction analysis. Interestingly, treatment of an another flexible ligand, [MePO(NH(3-Py))2] (L2), with the same Pd(II) acceptor resulted in exclusive formation of the trimeric cage [Pd3(L2)6·(BF4)6] (2).