The 'classical twin design' (CTD) circumvents parameter indeterminacy by assuming (1) negligible higher-order epistasis; and (2) either nonadditive genetic or common environmental effects are nonexistent, creating two potential sources of bias (Eaves et al., 1978; Grayson, 1989). Because the extended 'twin-family design' (ETFD) uses many more unique covariance observations to estimate parameters, common environmental and nonadditive genetic parameters can be simultaneously estimated. The ETFD thereby corrects for what is likely to be the largest of the two sources of bias in CTD parameter estimates (Keller & Coventry, 2005). In the current paper, we assess the extent of this and other potential sources of bias in the CTD by comparing all published ETFD parameter estimates to CTD parameter estimates derived from the same data. CTD estimates of the common environment were lower than ETFD estimates of the common environment for some phenotypes, but for other phenotypes (e.g., stature in females and certain social attitudes), what appeared as the common environment was resolved to be assortative mating in the ETFD. On average, CTD estimates of nonadditive genetic factors were 43% lower, and additive genetic factors 63% higher, than ETFD estimates. However, broad-sense heritability estimates from the CTD were only 18% higher than ETFD estimates, highlighting that the CTD is useful for estimating broad-sense but not narrow-sense heritability. These results suggest that CTD estimates can be misleading when interpreted literally, but useful, albeit coarse, when interpreted properly.