This paper studies Structural Vector Autoregressions identified using external instruments. These external instruments are taken to be correlated with the target shock (e.g., the oil instrument is relevant) and to be uncorrelated with other macroeconomic shocks of the model (e.g., the oil instrument is exogenous). The correlation between the external instrument and the target structural shock affects the validity of standard inference in large samples. With this observation in mind, we propose a new confidence set for the coefficients of the Structural Impulse-Response function and we show that its asymptotic confidence level is not affected by nuisance parameters. The implementation of our confidence set requires no more work than solving a single-variable quadratic equation. In an empirical application studying the dynamic effects of a structural oil shock using U.S. monthly data, we compare standard confidence sets with our inference procedure. As the theory suggests, we find substantial differences in cases where the external instrument is weakly correlated with the reduced form error in the oil price equation.