Theory-consistent models have to be kept small to be tractable. If they are to forecast well, they have to condition on data that are unmodelled, noisy, patchy and about the future. Agents can also use these data to form their own expectations. In this paper we illustrate a scheme for jointly conditioning the forecasts and internal expectations of linearised forward-looking DSGE models on data through a Kalman Filter fixed-interval smoother. We also trial some diagnostics of this approach, in particulardecompositions that reveal when a forecast conditioned on one set of variables implies estimates of other variables which are inconsistent with economic priors.