Current Spoken LanguageUnderstanding technology is based on a simple concept annotation of word sequences, where the interdependencies between concepts and their compositional semantics are neglected. This prevents an effective handling of language phenomena, with a consequential limitation on the design of more complex dialog systems. In this paper, we argue that shallow semantic representation as formulated in the Berkeley FrameNet Project may be useful to improve the capability of managing more complex dialogs. To prove this, the first step is to show that a FrameNet parser of sufficient accuracy can be designed for conversational speech. We show that exploiting a small set of FrameNetbased manual annotations, it is possible to design an effective semantic parser. Our experiments on an Italian spoken dialog corpus, created within the LUNA project, show that our approach is able to automatically annotate unseen dialog turns with a high accuracy.