In Dahl et al. (2007) we extended and refined some tools given in O'Hagan (2003) for criticism of Bayesian hierarchical models. Especially, avoiding double use of data by a data splitting approach was a main concern. Such tools can be applied at each node of the model, with a view to diagnosing problems of model fit at any point in the model structure. As in O'Hagan (2003) a Gaussian model of one-way analysis of variance was investigated. Through extensive MCMC simulations it was shown that our method detects model misspecification about as well as the one of O'Hagan, when this is properly calibrated, while retaining the desired false warning probability for data generated from the assumed model. In the present paper we suggest some new measures of conflict based on tail probabilities of the so-called integrated posterior distributions introduced in Dahl et al. (2007). These new measures are equivalent to the measure applied in the latter paper in simple Gaussian models, but seem more appropriately adjusted to deviations from normality and to conflicts not concerning location parameters. A general linear normal model with known covariance matrices is considered in detail.