The paper focuses on a novel bias-free least Squares (BFLS) parameter estimation approach which has recently received attention in the system identification and control literature. First, the BFLS parameter estimator is derived in a more general setting than in the original works. Then the paper goes on to show that any BFLS parameter estimator can be exactly realised in the well studied class of weighted instrumental variable (WIV) estimators. The paper also includes a comparative performance study of the unweighted estimators in the BFLS and IV classes.