If the system under test interacts with its environment at physically distributed ports, there is a separate independent tester at each port, and there is no global clock then we are testing in the distributed test architecture. It is known that the distributed test architecture can lead to additional controllability problems in which a tester cannot know when to send an input and this has led to most test generation techniques aiming to produce controllable test cases. However, there may be no controllable test case that achieves a given objective. This paper introduces the notion of a test section, in which each tester has a fixed input sequence to apply and there is no attempt to synchronise the testers. It defines the notion of a test section being convergent and shows how convergent test sections can be used as the basis of a less restrictive form of controllability.