The purpose of this paper is to make a quantitative contribution to the inflation versus price level targeting debate. It considers a policy-maker that can set policy either through an inflation targeting rule or a price level targeting rule to minimize a quadratic loss function using the actual projection model of the Bank of Canada (ToTEM). The paper finds that price level targeting dominates inflation targeting, although it can lead to much more volatile inflation depending on the weight assigned to output gap stabilization in the loss function. The price level targeting rule is also found to mimic the full-commitment solution quite well. There is, however, an important difference: the full-commitment solution does not require stationarity in the price-level. The paper then analyzes the extent to which the results are sensitive to Hansen and Sargent (2004) model uncertainty. The paper finds the price level targeting rule to be robust; its performance deteriorates slower than the inflation targeting rule and the absolute decline in performance is small in magnitude.