Comment: Second draft. 55 pages total and 22 pages main text. New results addedThis paper introduces an estimator that considerably weakens the conventional relevance condition of instrumental variable (IV) methods, allowing for instruments that are weakly correlated, uncorrelated, or even mean-independent but not independent of endogenous covariates. Under the relevance condition, the estimator achieves consistent estimation and reliable inference without requiring instrument excludability, and it remains robust even when the first moment of the disturbance term does not exist. In contrast to conventional IV methods, it maximises the set of feasible instruments in any empirical setting. Under a weak conditional median independence condition on pairwise differences in disturbances and mild regularity assumptions, identification holds, and the estimator is consistent and asymptotically normal.