In the case of external bleeding from penetrating trauma, you are always better off attempting to control hemorrhage with direct pressure. Consider a tourniquet only if bleeding cannot be controlled in that fashion.
Even if direct pressure fails, hemorrhage can often be controlled or lessened with direct arterial pressure proximal to the site of bleeding. The brachial artery can generally be controlled this way at mid upper arm level or at the elbow. The femoral artery likewise can be controlled with direct pressure, as can the popliteal at the knee. Controlling hemorrhage by direct proximal arterial pressure has the advantage of not completely disrupting the collateral circulation, and is less likely to cause nerve injury than a tourniquet.
Even if direct pressure fails, hemorrhage can often be controlled or lessened with direct arterial pressure proximal to the site of bleeding. The brachial artery can generally be controlled this way at mid upper arm level or at the elbow. The femoral artery likewise can be controlled with direct pressure, as can the popliteal at the knee. Controlling hemorrhage by direct proximal arterial pressure has the advantage of not completely disrupting the collateral circulation, and is less likely to cause nerve injury than a tourniquet.