Traits that are closely associated with fitness tend to have lower heritabilities (h2) than those that are not. This has been interpreted as evidence that natural selection tends to deplete genetic variation more rapidly for traits more closely associated with fitness (a corollary of Fisher's fundamental theorem), but Price and Schluter (1991) suggested the pattern might be due to higher residual variance in traits more closely related to fitness. The relationship between 10 different traits for females, seven traits for males, and overall fitness (lifetime recruitment) was quantified for great tits (Parus major) studied in their natural environment of Wytham Wood, England, using data collected over 39 years. Heritabilities and the coefficients of additive genetic and residual variance (CVA and CVR, respectively) were estimated using an "animal model." For both males and females, a trait's correlation (r) with fitness was negatively related to its h2 but positively related to its CVR. The CVA was not related to the trait's correlation with fitness in either sex. This is the third study using directly measured fitness in a wild population to show the important role of residual variation in determining the pattern of lower heritabilities for traits more closely related to fitness.