Results of additional improvements to the numerical solution methods used in RETRAN are presented. The new solution methods remove time-step size limitations associated with the four- and five-equation two-phase models in RETRAN. The four-equation, dynamic slip model is solved by a noniterative method that requires only one evaluation of a single matrix per time step. The five-equation, nonequilibrium model is solved by a two-step method. Calculations show that much larger time steps can be used with the new methods as compared with the standard methods.