In this paper, an in-depth analysis is undertaken into effective strategies for integrating the audio-visual speech modalities with respect to two major questions. Firstly, at what level should integration occur? Secondly, given a level of integration how should this integration be implemented? Our work is based around the well-known hidden Markov model (HMM) classifier framework for modeling speech. A novel framework for modeling the mismatch between train and test observation sets is proposed, so as to provide effective classifier combination performance between the acoustic and visual HMM classifiers. From this framework, it can be shown that strategies for combining independent classifiers, such as the weighted product or sum rules, naturally emerge depending on the influence of the mismatch. Based on the assumption that poor performance in most audio-visual speech processing applications can be attributed to train/test mismatches we propose that the main impetus of practical audio-visual integration is to dampen the independent errors, resulting from the mismatch, rather than trying to model any bimodal speech dependencies. To this end a strategy is recommended, based on theory and empirical evidence, using a hybrid between the weighted product and weighted sum rules in the presence of varying acoustic noise for the task of text-dependent speaker recognition.