Proof-Nets (Roorda 1990) are a good device for processing with categorial grammars, mainly because they avoid spurious ambiguities. Nevertheless, they do not provide easily readable structures and they hide the true proximity between Categorial Grammars and Dependency Grammars. We give here an other kind of Proof-Nets which is much related to Dependency Structures similar to those we meet in, for instance (Hudson 1984). These new Proof-Nets are called Connection Nets. We show that Connection Nets provide not only easily interpretable structures, but also that processing with them is more efficient. 1