This paper discusses the conditions for indentification with external instruments in Structural VARs under partial invertibility. We observe that in this case the shocks of interest and their effects can be recovered using an external instrument, provided that a condition of limited lag exogeneity holds. This condition is weaker than that required for LP-IV, and allows for recoverability of impact effects also une VAR misspecification. We assess our claims in a simulated environment, and provide an emirical application to the relevant cas of identification of monetary policy shocks.