Frequency hopping is a feature in GSM (Global System for Mobile Communications) cellular systems in which a frequency carrying the communication rapidly changes over time. This improves the overall capacity or the communication quality without the addition of new resources. The frequency hopping problem involves the determination of the subset of frequencies allocated to each cell to be used for frequency hopping, as well as determining the frequency hopping sequence of each radio in the network. This paper investigates this latter aspect for three levels of network synchronization. Heuristic procedures for evaluating and generating frequency hopping sequences are also proposed. Results from a real-life network indicate that by exploiting the control offered by higher synchronization levels, it is possible to significantly improve interference levels and to further take advantage of the gains offered by frequency hopping.