This paper considers whether the sticky information model of Mankiw and Reis (2002) can robustly deliver inflation inertia. I find that four features of the model play a key role in determining inflation inertia: the frequency of information updating, the degree of real rigidities, the nature and persistence of monetary policy, and the presence or not of information stickiness elsewhere in the economy. Real rigidities serve to dampen firms’ desired price changes and are a critical element in delivering inflation inertia. The type of monetary policy, money-growth vs. interest rate rules, also matters, with Taylor rules making inflation inertia less likely than under money growth rules. Adding sticky information in consumption to the model yields a more gradual adjustment of output, thereby decreasing the incentive for firms to change prices on impact and increasing the inertia of inflation. I also explore the implications of using random versus fixed durations of information rigidity and argue that with the latter, the choice of the policy rule has a smaller effect on the qualitative response of inflation. These results allow us to sort out some conflicting conclusions on inflation inertia in sticky information models and suggest that inertia is more sensitive to parameter choices than previously thought.