Pesaran and Smith (2011) concluded that DSGE models were sometimes a straitjacket which hampered the ability to match certain features of the data. In this paper we look at how one might assess the fit of these models using a variety of measures, rather than what seems to be an increasingly common device - the Marginal Data Density. We apply these in the context of models by Christiano et.al (2014) and Ireland (2004), finding they fail to make a match by a large margin. Against this, there is a strong argument for having a straitjacket as it enforces some desirable behaviour on models and makes researchers think about how to account for any non-stationarity in the data. We illustrate this with examples drawn from the SVAR literature and also more eclectic models such as Holston et al (2017) for extracting an estimate of the real natural rate.