Decentralised tests appear in the context of information processing from distributed sensors. A decentralised test is composed of peripheral tests and a fusion rule. While the peripheral tests yield decisions at the individual sensors, the fusion rule operates on the peripheral decisions to provide the final decision. To find a most powerful decentralised test, i.e. one with maximal probability of detection subject to a given false alarm probability, the peripheral tests and fusion rule must be optimised simultaneously. For the case of two sensors deciding on independent observations, it is demonstrated that there is a most powerful decentralised test in which the fusion rule is either the AND or the OR rule.