Some systems may be modelled as a set of communicating finite state machines with a slow environment. These machines communicate through the exchange of values. While it is possible to convert such a model into one finite state machine, from which test cases can be derived, this process may lead to an explosion in the number of states. Alternatively it is possible to utilise any independence that exists. The problem of producing a minimal test set, in the presence of certain types of independence and unique input/output sequences, can be represented as a variant of the vehicle routing problem. Possible heuristics for solving this problem are outlined and the method is applied to an example.