We present an extension of the πI-calculus with formal sums of terms. A study of the properties of this sum reveals that its neutral element 0 can be used to make assumptions about the behaviour of the environment of a process. From this observation we derive an enriched calculus that enjoys a confluent reduction which preserves the testing semantics of processes. This system is shown to be strongly normalising for terms without replication, and the study of its normal forms provides fully abstract trace semantics for testing of πI processes.