Coumadin is the most potent blood thinner, and works by reducing the amount of clotting factors (proteins) in your blood. The other agents act by inhibiting the function of platelets, cell fragments in your bloodstream which can help blood to clot. Clopidogrel is next in line, and when used with aspirin, is not far behind Coumadin in its ability to make you bleed. Aspirin and the NSAIDs follow in bleeding potential. You should also know that some prescription drugs, including antidepressants like Zoloft (sertraline), as well as nonprescription supplements such as fish oil and ginseng, can increase your risk of bleeding.