This paper analyzes the theoretical problem of the real option with barrier. It models an investment decision with a double irreversibility concern: investing is irreversible, but waiting runs the risk of loosing the opportunity to invest. The optimal strategy leads to earlier investment when the barrier increases, or when uncertainty decreases. Uncertainty has ambiguous effects on the expected decision time and on the investment probability after N years. Analytical and numerical results also apply to the perpetual American call with a down-and-out barrier on a dividend paying asset.