This paper starts from the observation that parameter instability and model uncertainty are relevant problems for the analysis of monetary policy in small macroeconomic models. We propose to deal with these two problems by implementing a novel ‘thick recursive modelling’ approach. At each point in time we estimate all models generated by the combinations of a base-set of k observable regressors for aggregate demand and supply. We compute optimal monetary policies for all possible models and consider alternative ways of summarizing their distribution. Our main results show that thick recursive modelling delivers optimal policy rates that track the observed policy rates better than the optimal policy rates obtained under a constant parameter specification, with no role for model uncertainty.