In the course of a (man-machine) dialogue, the system's belief concerning the user's intention is continuously being built up. Moreover, restricting the discourse to a narrow application domain further constrains the variety of possible user reactions. In this paper, we will show how these knowledge sources may be utilized in a stochastic framework to improve speech understanding. On field-test data collected with our automatic exchange board prototype PADIS1, a relative reduction of attribute errors by 27% has been obtained.