In ATM networks, a user should negotiate at connection set-up a traffic contract which includes traffic characteristics and requested QoS. The traffic characteristics currently considered are the Peak Cell Rate, the Sustainable Cell Rate, the Intrinsic Burst Tolerance and the Cell Delay Variation (CDV) tolerance(s). The values taken by these traffic parameters characterize the so-called ''Worst Case Traffic'' that is used by CAC procedures for accepting a new connection and allocating resources to it. Conformance to the negotiated traffic characteristics is defined, at the ingress User to Network Interface (UNI) and at subsequent Inter Carrier Interfaces (ICIs), by algorithmic rules based on the Generic Cell Rate Algorithm (GCRA) formalism. Conformance rules are implemented by policing mechanisms that control the traffic submitted by the user and discard excess traffic. It is therefore essential to set traffic characteristic values that are relevant to the considered cell stream, and that ensure that the amount of non-conforming traffic is small. Using a queueing model representation for the GCRA formalism, several methods are available for choosing the traffic characteristics. This paper presents approximate methods and discusses their applicability. We then discuss the problem of obtaining traffic characteristic values for a connection that has crossed a series of switching nodes. This problem is particularly relevant for the traffic contract components corresponding to ICIs that are distant from the original source.