Two different models of the influence of the stop voicing on F0 are identified. The more widely accepted of the two, called the rise-fall dichotomy, claims that F0 falls after voiceless stops but rises after voiced stops, and that the direction of post-release F0 is contextually invariant. The alternative model, referred to as the no-rise view, arose from recent production studies. It claims that the onset frequency of post-release F0 is raised after all stops, though only relatively little if they are phonologically voiced. More importantly, it sees F0 contours as a combination of segmental perturbations added onto a smooth underlying intonation contour. Consequently the direction of post-release F0 depends not only on segmental phonetic features but also on the prosodic structure. In three perceptual experiments utilising computer-synthesised intervocalic bilabial stops, opposing predictions of the two models are tested by embedding falling, level, and rising perturbations in different intonational environments. In each experiment the predictions of the no-rise view are supported and those of the rise-fall dichotomy are falsified. The conclusion drawn is that investigations of segmental phonetics can give rise to misleading results unless the accompanying prosodic structure is also taken into account.