The standard approach to HMM-based speech synthesis is inconsistent in the enforcement of the deterministic constraints between static and dynamic features. The trajectory HMM and autoregressive HMM have been proposed as normalized models which rectify this inconsistency. This paper investigates the practical effects of using these normalized models, and examines the strengths and weaknesses of the different models as probabilistic models of speech. The most striking difference observed is that the standard approach greatly underestimates predictive variance. We argue that the normalized models have better predictive distributions than the standard approach, but that all the models we consider are still far from satisfactory probabilistic models of speech. We also present evidence that better intra-frame correlation modelling goes some way towards improving existing normalized models.