A critical evaluation of assumptions made in the converging flow analysis of Cogswell is made, and a refined analysis is given by relaxing two of these assumptions. This reexamination of the Cogswell method was motivated by some recent encouraging comparative studies by Laun and Schuch of conventional extensional results and converging flow data. Of the two assumptions relaxed in the analysis. the relaxation of the assumption of a constant extensional viscosity above the orifice, into which the converging flow takes place, is shown to be primarily responsible for the substantially improved agreement with conventional extensional viscosity measurements. Because the variation of the extensional viscosity above the orifice is not known, solution of the equations is not given in closed form, and their solution is solved by an iterative procedure. The good agreement of the results of the modified converging flow analysis given here with conventional extensional measurements over a large range of rates demonstrates that converging flow methods can provide an accurate and relatively routine method of measuring extensional viscosity in molten polymers.