We study the speed of price reactions to positive and negative demand and costs shocks. In line with the predictions of optimal price setting models, we find that price adjustment lags vary with firm's characteristics that are related to the importance of menu costs, the variability of the optimal price, and the sensitivity of profits to sub-optimal prices. We also find that the majority of firms react faster to positive than to negative cost shocks, and more quickly to negative than to positive demand shocks. However, the direction and magnitude of these asymmetries vary across firms and with the type of shock in a way that cannot be fully explained by any single theoretical model of asymmetric price adjustment. Overall, these results suggest that the reaction to monetary policy shocks may depend on which firms or sectors are particularly affected by them and, therefore, that richer models are needed to fully understand the effects of monetary policy.