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We present a method for text compression, which relies on pruning of a syntactic tree. The syntactic pruning applies to a complete analysis of sentences, performed by a French dependency grammar. Sub-trees in the syntactic analysis are pruned when they are labelled with targeted relations. Evaluation is performed on a corpus of sentences which have been manually compressed. The reduction ratio of extracted sentences averages around 70%, while retaining grammaticality or readability in a proportion of over 74%. Given these results on a limited set of syntactic relations, this shows promise for any application which requires compression of texts, including text summarization.