We present an extension of the pi-I-calculus with formal sums of terms. A study of the properties of this sum reveals that its neutral element can be used to make assumptions about the behaviour of the environment of a process. Furthermore, the formal sum appears as a fundamental construct that can be used to decompose both internal and external choice. From these observations, 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 pi-I processes.