This paper looks at whether sticky-price New Keynesian models with microfounded inertia can usefully describe U.S. data. I estimate a range of models, considering specifications with either internal or external consumption habits, specifications containing Taylor-type rules or an optimal discretionary rule, and specifications where inflation is driven by movements in the gap or real marginal costs. Among other results, I find that models with external habits produce very similar aggregate behavior to models with internal habits. I also find that modeling monetary policy in terms of an optimal discretionary rule describes U.S. data as well as a forward-looking Taylor-type rule does, and that the data favor the traditional gap-based Phillips curve over specifications containing real marginal costs.