Several notions of non-interference have been proposed in the literature for studying the problem of confidentiality in concurrent systems. The common feature of these non-interference properties is that they are all defined as extensional properties based on some notion of behavioural equivalence on systems. Here, instead, we address the problem of defining non-interference by looking at the structure of the systems under investigation. We use a simple class of Petri nets, namely, contact-free elementary net systems, as the system model and define structural non-interference properties based on the absence of particular places in the net: such places show that a suitable causality or conflict relation is present between a high-level transition and a low-level one. We characterise one structural property, called PBNI+, which we show to be equivalent to the well-known behavioural property SBNDC. It essentially captures all the positive information flows (that is, a low-level user can deduce that some high-level action has occurred). We start by providing a characterisation of PBNI+ on contact-free elementary net systems, then extend the definition to cope with the richer class of trace nets.