Social security plays an essential role in an economy, but if designed incorrectly can distort the labor supply and savings behavior of individuals in the economy. We explore how well the Australian means-tested pension system provides social insurance by calculating possible welfare gains from changing the settings in the current means-tested pension system. This work has been explored by other researchers both in Australia and in other pension-providing economies. However, most research ignores the fact that welfare gains can be found by reducing the cost of the program. To exclude these welfare costs, this paper fixes the cost of the system. We find that the means-tested pension system is welfare reducing, but does provide a better outcome than an equivalent-costing PAYG system. We also find that if the benefit amount is held constant, and hence the cost of the pension program is allowed to vary, a taper rate of 1.0 is optimal. However, once we fix this cost, a universal benefit scheme provides the best welfare outcome.