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Pesaran and Smith (2011) concluded that Dynamic Stochastic General Equilibrium (DSGE) models were sometimes a straitjacket which hampered the ability to match certain features of the data. In this chapter, the authors 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. The authors apply these in the context of models by Christiano, Motto, and Rostagno (2014) and Ireland (2004), finding they fail to make a match by a large margin. Both of these models feature more shocks than observed variables, resulting in the empirical shocks having a singular density, and so making them correlated. When correlated one can neither interpret impulse responses nor perform variance decompositions. Against this, there is a strong argument for having a straitjacket, as it enforces some desirable behavior on models and makes researchers think about how to account for any non-stationarity in the data. The authors illustrate this with examples drawn from the SVAR literature and also more eclectic models such as Holston, Laubach, and Williams (2017) for extracting an estimate of the real natural rate.