This paper describes a simple discourse parsing and analysis algorithm that combines a formal underspecification utilising discourse grammar with Information Retrieval (IR) techniques. First, linguistic knowledge based on discourse markers is used to constrain a totally underspecified discourse representation. Then, the remaining underspecification is further specified by the computation of a topicality score for every discourse unit. This computation is done via the vector space model. Finally, the sentences in a prominent position (e.g. the first sentence of a paragraph) are given an adjusted topicality score. The proposed algorithm was evaluated by applying it to a text summarisation task. Results from a psycholinguistic experiment, indicating the most salient sentences for a given text as the ‘gold standard’, show that the algorithm performs better than commonly used machine learning and statistical approaches to summarisation.