This paper examines several modified versions of the heteroskedasticity-consistent covariance matrix estimator, focusing on their finite sample properties. The authors compare the performance of quasi-$t$ statistics derived from these estimators through sampling experiments. They find that the jackknife-based estimator (HC$_3$) outperforms the original HC estimator and other modified estimators in small samples. Additionally, they explore the use of modified critical values based on Edgeworth approximations, which generally perform well, especially with larger sample sizes. The paper also evaluates the power of various tests for heteroskedasticity, suggesting that the heteroskedasticity-consistent covariance matrix estimator (HC$_3$) may be more reliable even when heteroskedasticity is not detected. The authors conclude that HC$_3$ is the preferred choice among the modified estimators and that it can provide more accurate inferences in the presence of heteroskedasticity, even when the sample size is small.This paper examines several modified versions of the heteroskedasticity-consistent covariance matrix estimator, focusing on their finite sample properties. The authors compare the performance of quasi-$t$ statistics derived from these estimators through sampling experiments. They find that the jackknife-based estimator (HC$_3$) outperforms the original HC estimator and other modified estimators in small samples. Additionally, they explore the use of modified critical values based on Edgeworth approximations, which generally perform well, especially with larger sample sizes. The paper also evaluates the power of various tests for heteroskedasticity, suggesting that the heteroskedasticity-consistent covariance matrix estimator (HC$_3$) may be more reliable even when heteroskedasticity is not detected. The authors conclude that HC$_3$ is the preferred choice among the modified estimators and that it can provide more accurate inferences in the presence of heteroskedasticity, even when the sample size is small.