Songs of passerines are generally complex, long-range acoustic signals, and are highly diverse across species. This diversity must nevertheless be shaped by the capabilities of the avian vocal physiology. For example, within species, loudness has been shown to trade-off with aspects of song complexity. Here, I ask if such trade-offs with loudness influenced the evolutionary diversification of song among passerines. Comparing perceived song loudness across > 140 European and North American species showed that loudness is positively related to body size and to singing with simple trilled syntax, and negatively related to aspects of syllable complexity. Syntax and syllable phonology together explained more variation than body size did, indicating that the acoustic design of songs is an important factor determining loudness. These results show for the first time that loudness covaries with, and possibly limits, song complexity across species, suggesting that a trade-off with loudness shaped the evolutionary diversification of passerine song.