In this paper we present an analysis of the limited-$1$ polling policy in Bluetooth piconets employing multislot packets. We characterize the network performance in terms of achievable rate regions and packet delay distribution, where the latter is derived for the case of arrivals forming a marked Poisson point process. In a balanced scenario, our analysis provides exact expressions for the mean packet delay, improving existing results based on the theory of $M|G|1$ queues with vacations. A further approximation, based on a renewal argument, is then proposed. It is shown to succesfully track the system behavior (even when the network approaches saturation) leading at the same time to a simple closed–form expression for the average packet delay.