The analysis of monetary policy rules has been confined to models not capable of examining situations where an economy is converging to a higher balanced growth path. For the small open economies having entered the European Union recently this is however a very relevant question. The main aim of their integration is convergence itself and most of the criteria they have to fulfil in order to become members of the euro zone are of monetary nature. It is thus of special interest for them whether and how the chosen strategy of monetary policy aiming at the fulfilment of the requirements they face affects the transition. In this paper a first attempt is made to compare monetary policy rules in a monetary model of small open economies, which builds essentially on the convergence literature. The results show that the economy behaves very differently in the transition under the different monetary policy rules examined.