We present an approach to automatically identifying the arguments of discourse connectives based on data from the Penn Discourse Treebank. Of the two arguments of connectives, called Arg1 and Arg2, we focus on Arg1, which has proven more challenging to identify. Our approach employs a sentence-based representation of arguments, and distinguishes intra-sentential connectives, which take both their arguments in the same sentence, from inter-sentential connectives, whose arguments are found in different sentences. The latter are further distinguished by paragraph position into ParaInit connectives, which appear in a paragraph-initial sentence, and ParaNonInit connectives, which appear elsewhere. The paper focusses on predicting Arg1 of Inter-sentential ParaNonInit connectives, presenting a set of scope-based filters that reduce the search space for Arg1 from all the previous sentences in the paragraph to a subset of them. For cases where these filters do not uniquely identify Arg1, coreference-based heuristics are employed. Our analysis shows an absolute 3 % performance improvement over the high baseline of 83.3 % for identifying Arg1 of Inter-sentential ParaNonInit connectives. 1.