It has been discovered that improved polystyrene products may be obtained by polymerizing styrene in the presence of at least one multifunctional initiator, at least one chain transfer agent, and at least one cross-linking agent. The presence of the multifunctional initiator tends to cause more branched structures in the polystyrene. A mathematical model that helps optimize the levels of these additives for given molecular weights, melt flow indices (MFIs) and zero shear viscosities (eta0) has also been discovered.