Animal vocalizations play an important role in individual recognition, kin recognition, species recognition, and sexual selection. Despite much work in these fields done on birds virtually nothing is known about the heritability of vocal traits in birds. Here, we study a captive population of more than 800 zebra finches (Taeniopygia guttata) with regard to the quantitative genetics of call and song characteristics. We find very high heritabilities in nonlearned female call traits and considerably lower heritabilities in male call and song traits, which are learned from a tutor and hence show much greater environmental variance than innate vocalizations. In both sexes, we found significant heritabilities in several traits such as mean frequency and measures of timbre, which reflect morphological characteristics of the vocal tract. These traits also showed significant genetic correlations with body size, as well as positive genetic correlations between the sexes, supporting a scenario of honest signaling of body size through genetic pleiotropy ("index signal"). In contrast to such morphology-related voice characteristics, classical song features such as repertoire size or song length showed very low heritabilities. Hence, these traits that are often suspected to be sexually selected would hardly respond to current directional selection.