Body size is a key sexually selected trait in many animal species. If size imposes a physical limit on the production of loud low-frequency sounds, then low-pitched vocalisations could act as reliable signals of body size. However, the central prediction of this hypothesis--that the pitch of vocalisations decreases with size among competing individuals--has limited support in songbirds. One reason could be that only the lowest-frequency components of vocalisations are constrained, and this may go unnoticed when vocal ranges are large. Additionally, the constraint may only be apparent in contexts when individuals are indeed advertising their size. Here we explicitly consider signal diversity and performance limits to demonstrate that body size limits song frequency in an advertising context in a songbird. We show that in purple-crowned fairy-wrens, Malurus coronatus coronatus, larger males sing lower-pitched low-frequency advertising songs. The lower frequency bound of all advertising song types also has a significant negative relationship with body size. However, the average frequency of all their advertising songs is unrelated to body size. This comparison of different approaches to the analysis demonstrates how a negative relationship between body size and song frequency can be obscured by failing to consider signal design and the concept of performance limits. Since these considerations will be important in any complex communication system, our results imply that body size constraints on low-frequency vocalisations could be more widespread than is currently recognised.