Bluetooth is a low-power, low-cost, short-range wireless communication system operating in the 2.4-GHz industrial, scientific, and medical (ISM) band. Bluetooth links use frequency hopping whereby each packet is sent on a single frequency while different packets are sent on different frequencies. Further, there are a limited number of packet sizes. We show that we can exert indirect control over transmission conditions by choosing the packet size transmitted over each frequency as a function of the channel conditions. Our goal then is to provide a packet-size-selection algorithm that can maximize the throughput in a Bluetooth piconet in the presence of lossy wireless channels. We first develop a renewal-theory-based mathematical model of packet transmission in a frequency-hopping system such as a Bluetooth piconet. We use this model to show that a threshold-based algorithm for choosing the packet lengths maximizes the throughput of the system. We provide an algorithm that determines the optimal thresholds efficiently. We show the optimality of this algorithm without using standard optimization techniques, since it is not clear that these techniques would be applicable given the functions involved. Using simulations, we observe that this strategy leads to significantly better throughput as compared to other baseline strategies, even if the assumptions made to prove optimality are relaxed.