Bluetooth is an emerging standard for short range, low cost, low power wireless access technology. The Bluetooth technology is just starting to appear on the market and there is an urgent need to enable new applications with real time constraints to run on top of Bluetooth devices. The Bluetooth Specification proposes a Round Robin scheduler as possible solution for scheduling the transmissions in a Bluetooth Piconet. However, this basic scheme performs badly under asymmetric traffic conditions. Recently, several polling schemes have been proposed to improve performance on asymmetric transmissions and to support bandwidth guarantee. However, there is no solution available to support both delay and bandwidth guarantees required by real time applications. In this paper, we present FPQ, (Fair and efficient Polling algorithm with QoS support) a new polling algorithm for Bluetooth Piconet that supports both delay and bandwidth guarantees and aims to remain fair and efficient with asymmetric flow rates. We present an extensive set of simulations and provide performance comparisons with other polling algorithms. Our performance study indicates that FPQ, while supporting flow rate and maximum delay QoS requests, outperforms Deficit Round Robin in term of delays by at least 10 in all cases, sometimes by more than 30 Moreover, FPQ was designed to take the specifics of Bluetooth into considerati- on, in particular the low complexity required for cheap implementation.