Over the past decade and a half, several lines of research have investigated aspects of the smooth signalling redundancy hypothesis. This hypothesis proposes that speakers distribute the information in linguistic utterances as evenly as possible, in order to make the utterance more robust against noise for the hearer. Several studies have shown evidence for this hypothesis in limited linguistic domains, showing that speakers manipulate acoustic and syntactic features to avoid drastic spikes or troughs in information content. In theory, the mechanism behind this is that these spikes would make utterances more vulnerable to noise events, and thus, communicative failure. However, this previous work doesn't consider information density across entire utterances, and only rarely has this mechanism been directly explored. Here, we introduce a new descriptive statistic that quantifies the uniformity of information across an entire utterance, alongside an algorithm that can measure the uniformity of actual utterances against an optimized distribution. Using a simple simulation, we show that utterances optimized for more uniform distributions of information are, in fact, more robust against noise.