Sound onsets dominate spatial judgments of many types of periodic sound. Conversely, ongoing cues often dominate in spatial judgments of aperiodic noise. This study quantified onset dominance as a function of both the bandwidth and the temporal regularity of stimuli by measuring temporal weighting functions (TWF) from Stecker, Ostreicher, and Brown [(2013) J. Acoust. Soc. Am. 134, 1242-1252] for lateralization of periodic and aperiodic noise-burst trains. Stimuli consisted of 16 noise bursts (1 ms each) repeating at an interval of 2 or 5 ms. TWFs were calculated by multiple regression of lateralization judgments onto interaural time and level differences, which varied independently ( ±100 μs, ±2 dB) across bursts. Noise tokens were either refreshed on each burst (aperiodic) or repeated across sets of 2, 4, 8, or 16 bursts. TWFs revealed strong onset dominance for periodic noise-burst trains (16 repeats per token), which was markedly reduced in aperiodic trains. A second experiment measured TWFs for periodic but sinusoidally amplitude-modulated noise burst trains, revealing greater weight on the earliest and least intense bursts of the rising envelope slope. The results support the view that envelope fluctuations drive access to binaural information in both periodic and aperiodic sounds.