Experimental results have previously suggested that the transmetalation step in the Stille reaction is hindered at one extreme by very bulky ligands L on the PdL2 catalyst, yet at the other extreme, transmetalation is also found to be slow for small ligands. Our aim in this paper is to resolve this dilemma using computational chemistry and to show which ligand is best and why. With the use of density functional theory we show that the reason why L = (PBu3)-Bu-t retards transmetalation is because the bulky ligand hinders the coordination of the organostannane. On the other hand a small ligand such as L = PMe3 leads to the formation of a very stable intermediate in the catalytic cycle which then requires a large activation energy for the transmetalation to proceed. The L = PPh3 ligand appears to provide just the,right balance in that it can readily coordinate the organostannane but avoids forming the very stable intermediate, and is thus the ligand of choice. L = PPh2Me is predicted to be the next best option, but L = PPhMe2 is too small and forms an intermediate whose stability prevents further reaction in the transmetalation step. Our calculations are also able to account for the accelerating role of CsF in the transmetalation step of the Stille reaction. Finally, this work demonstrates the importance of taking into account the steric properties of the full ligand in theoretical studies of such reactions, rather than using small model phosphines.