The International Atomic Energy Agency Coordinated Research Project, "Benchmark Analyses of an EBR-II Shutdown Heat Removal Test" is in the third year of its four-year term. Nineteen participants representing eleven countries have simulated two of the most severe transients performed during the Shutdown Heat Removal Tests program conducted at Argonne's Experimental Breeder Reactor II. Benchmark specifications were created for these two transients, enabling project participants to develop computer models of the core and primary heat transport system, and simulate both transients. In phase 1 of the project, blind simulations were performed and then evaluated against recorded data. During phase 2, participants have refined their models to address areas where the phase 1 simulations did not predict the experimental data as well as desired. This paper describes the progress that has been made to date in phase 2 in improving on the earlier simulations and presents the direction of planned work for the remainder of the project.