Since 2012 Eurostat requires the national statistical institutes (NSIs) in all European Union (EU) countries to compute official House Price Indices (HPIs) at a quarterly frequency. Eurostat recommends computing the HPI using a hedonic method. Most NSIs have followed this advice, although they differ in their choice of method. Some NSIs use stratified medians instead of hedonic methods. We evaluate the theoretical and empirical properties of these methods. Of particular concern is the comparability of the HPIs across countries when computed using different methods. Our empirical comparisons use detailed micro-level data sets for Sydney and Tokyo, containing about 867,000 actual housing transactions. All the hedonic methods perform better than stratified medians. The hedonic methods generate quite similar results, except when applied to new dwellings in Tokyo. This finding shows that the choice of hedonic method can become important for smaller data sets. Also, the widely used hedonic repricing method becomes unreliable when the reference shadow prices are not updated frequently.