We introduce two simple new variants of the jackknife instrumental variables (JIVE) estimator for overidentified linear models and show that they are superior to the existing JIVE estimator, significantly improving on its small-sample-bias properties. We also compare our new estimators to existing Nagar (1959) type estimators. We show that, in models with heteroskedasticity, our estimators have superior properties to both the Nagar estimator and the related B2SLS estimator suggested in Donald and Newey (2001). These theoretical results are verified in a set of Monte Carlo experiments and then applied to estimating the returns to schooling using actual data. Copyright by the President and Fellows of Harvard College and the Massachusetts Institute of Technology.