Researchers studying the evolution of animal communication often ask what generates and maintains signal complexity, but they define and measure complexity in different ways. If different metrics are not concordant, then studies using them are probably not comparable. In this study, we asked whether 7 metrics of bird song complexity vary in tandem among individuals of a single species, the Rock Wren (Salpinctes obsoletus). The included metrics were chosen because they are regularly used by researchers in the field to test hypotheses within the literature. Results indicated that none of the metrics positively correlated with any others, suggesting that bird songs are not under general selective pressures favoring increased complexity across multiple features. If metrics of signal complexity are not correlated, then care should be taken when designing analyses and comparing results. Researchers should always clearly define the “complexity” under investigation and verify that it has significance to the study species. Contradictory outcomes among existing research into signal “complexity” may result from the fact that this single word is used to represent multiple independent traits.