Using external instruments one can recover the effects of individual shocks without fully identifying a VAR. We show that fully or almost fully instrumenting a VAR--that is, using an instrument for each shock--allows one to overidentify the model by incorporating the condition that the structural shocks are uncorrelated, via GMM. We apply our approach to a fiscal VAR for the US over 1948-2019, where the overidentifying restrictions are not rejected. The overidentified SVAR yields (a) greater precision in estimating impulse response functions and multipliers and (b) measures of the effects of non-fiscal shocks even when there is no instrument for them.