This paper proposes two models in which price stickiness arises endogenously even though firms are free to change their prices at zero physical cost. Firms are subject to idiosyncratic and aggregate shocks, and they also face a risk of making errors when they set their prices. In our first specification, firms are assumed to play a dynamic logit equilibrium, which implies that big mistakes are less likely than small ones. The second specification derives logit behavior from an assumption that precision is costly. The empirical implications of the two versions of our model are very similar. Since firms making sufficiently large errors choose to adjust, both versions generate a strong "selection effect" in response to a nominal shock that eliminates most of the monetary nonneutrality found in the Calvo model. Thus the model implies that money shocks have little impact on the real economy, as in Golosov and Lucas (2007), but fits microdata better than their specification. JEL Classification: E31, D81, C72.