Frequency- and amplitude-modulated (FM and AM) sounds are the building blocks of complex sounds. In the present study, we investigated the ability of human observers to process spatial information in an important class of FM sounds: broadband directional sweeps common in natural communication signals such as speech. The stimuli consisted of linear or logarithmic unidirectional FM pulses that swept either up or down in frequency at various rates. Spatial localization thresholds monotonically improved as sweep duration decreased and as sweep rate increased, but no difference in performance was observed between logarithmic and linear or between up- and down-frequency sweeps. Counterintuitive reversals in localization were observed which suggested that the localization of high-frequency sweeps may be strongly dominated by amplitude information even in situations in which one might consider timing cues to be critical. Implications of these findings for the localization of complex sounds are discussed.