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Within a frequentist SEM framework, adjudicating model quality through measures of fit has been an active area of methodological research. Exacerbating this conversation is research revealing that higher quality measurement portions of a SEM can result in poorer estimates of overall model fit than lower quality measurement models, given the same structural misspecifications. Through population analysis and Monte Carlo simulations we extend this conversation to recently developed Bayesian measures of fit to evaluate whether they are adversely susceptible to the same consequences in the context of both uninformative and informative priors. Results indicate that Bayesian measures of fit show many of the same behaviors as their frequentist cousins. Strategies for their usefulness in practice will be discussed.